Denoising Diffusion Probabilistic Models Jonathan Ho Ajay Jain Pieter Abbeel UC Berkeley UC Berkeley UC Berkeley jonathanho@berkeley.edu ajayj@berkeley.edu - 中英文对照
Denoising Diffusion Probabilistic Models Jonathan Ho Ajay Jain Pieter Abbeel UC Berkeley UC Berkeley UC Berkeley jonathanho@berkeley.edu ajayj@berkeley.edu - 中英文对照
中英文对照
<a id="S0001"></a> Source: p.1 S0001
Original: Denoising Diffusion Probabilistic Models Jonathan Ho Ajay Jain Pieter Abbeel UC Berkeley UC Berkeley UC Berkeley jonathanho@berkeley.edu ajayj@berkeley.edu pabbeel@cs.berkeley.edu Abstract We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics.
中文: Jonathan Ho Ajay Jain Pieter Abbeel UC 伯克利 UC 伯克利 UC 伯克利 Jonathanho@berkeley.edu ajayj@berkeley.edu pabbeel@cs.berkeley.edu 摘要 我们利用扩散概率模型呈现出高质量的图像合成结果,这种模型是由无平衡热力学的考虑所激发的一类潜在可变模型。
<a id="S0002"></a> Source: p.1 S0002
Original: Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding.
中文: 我们的最佳成果是通过按照扩散概率模型和去诺比分与Langevin动力学之间的一个新联系设计的加权变异约束培训,我们的模式自然承认一种递增的减压方案,可以被解释为自旋解码的概括.
<a id="S0003"></a> Source: p.1 S0003
Original: On the unconditional CIFAR10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art FID score of 3.17.
中文: 在无条件的CIFAR10数据集上,我们获得9.46分的入场分和3.17分的全能FID分.
<a id="S0004"></a> Source: p.1 S0004
Original: On 256x256 LSUN, we obtain sample quality similar to ProgressiveGAN.
中文: 在256x256 LSUN上,我们获得了类似于进步GAN的样本质量.
<a id="S0005"></a> Source: p.1 S0005
Original: Our implementation is available at https://github.com/hojonathanho/diffusion. 1 Introduction Deep generative models of all kinds have recently exhibited high quality samples in a wide variety of data modalities.
中文: 我们的执行情况可查阅https://github.com/hojonathanho/diffusion。 1 各种深层遗传模型最近以各种各样的数据方式展示了高质量的样本。
<a id="S0006"></a> Source: p.1 S0006
Original: Generative adversarial networks (GANs), autoregressive models, flows, and variational autoencoders (VAEs) have synthesized striking image and audio samples [14, 27, 3, 58, 38, 25, 10, 32, 44, 57, 26, 33, 45], and there have been remarkable advances in energy-based modeling and score matching that have produced images comparable to those of GANs [11, 55].
中文: 基因对抗网络(GANs),自递式模型,流出和变相自编码器(VAEs)已合成出惊人的图像和音频样本[14,27,3,58,38,25,10,32,44,57,26,33,45],在以能为基础的模型和分数匹配方面有显著的进步,产生了与GANs[11,55]相当的图像.
<a id="S0007"></a> Source: p.1 S0007
Original: Figure 1: Generated samples on CelebA-HQ 256 × 256 (left) and unconditional CIFAR10 (right) 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada. 0202 ceD 61 ]GL.sc[ 2v93211.6002:viXra
中文: 图1:加拿大温哥华CelebA-HQ256×256(左)和无条件的CIFAR10(右)神经信息处理系统第34次会议(2020年)上生成的样本。 0202 ceD 61]GL.sc[2v93211.6002:viXra
<a id="S0008"></a> Source: p.2 S0008
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<a id="S0009"></a> Source: p.2 S0009
Original: 1) Figure 2: The directed graphical model considered in this work.
中文: 1) 图2:本作中考虑的定向图形模型.
<a id="S0010"></a> Source: p.2 S0010
Original: This paper presents progress in diffusion probabilistic models [53]. A diffusion probabilistic model (which we will call a “diffusion model” for brevity) is a parameterized Markov chain trained using variational inference to produce samples matching the data after finite time.
中文: 本文件介绍了传播概率模型方面的进展[53]。 传播概率模型(我们将称之为“散射模型”,用于简洁性)是一个参数化的马可夫链条,利用可变推论在有限时间后产生匹配数据的样品。
<a id="S0011"></a> Source: p.2 S0011
Original: Transitions of this chain are learned to reverse a diffusion process, which is a Markov chain that gradually adds noise to the data in the opposite direction of sampling until signal is destroyed.
中文: 这个链子的过渡被学习来倒转一个扩散过程,这是一个马尔可夫链子,它逐渐地将噪声添加到数据中以相反的取样方向,直到信号被破坏.
<a id="S0012"></a> Source: p.2 S0012
Original: When the diffusion consists of small amounts of Gaussian noise, it is sufficient to set the sampling chain transitions to conditional Gaussians too, allowing for a particularly simple neural network parameterization.
中文: 当扩散由少量高斯噪声所组成时,就足以将采样链向有条件的高斯噪声的过渡也设定下来,从而可以实现特别简单的神经网络参数化.
<a id="S0013"></a> Source: p.2 S0013
Original: Diffusion models are straightforward to define and efficient to train, but to the best of our knowledge, there has been no demonstration that they are capable of generating high quality samples.
中文: 传播模型可以直截了当地定义和高效地训练,但据我们所知,还没有证明它们能够产生高质量的样本。
<a id="S0014"></a> Source: p.2 S0014
Original: We show that diffusion models actually are capable of generating high quality samples, sometimes better than the published results on other types of generative models (Section 4).
中文: 我们显示,传播模型实际上能够产生出高质量的样本,有时比其他类型基因模型上公布的结果更好(第4节).
<a id="S0015"></a> Source: p.2 S0015
Original: In addition, we show that a certain parameterization of diffusion models reveals an equivalence with denoising score matching over multiple noise levels during training and with annealed Langevin dynamics during sampling (Section 3.2) [55, 61].
中文: 此外,我们显示,传播模型的某些参数化显示,在训练期间,在多噪声水平上进行去诺分比,在取样期间进行厌杀Langevin动力学比对(第3.2节)[55,61]。
<a id="S0016"></a> Source: p.2 S0016
Original: We obtained our best sample quality results using this parameterization (Section 4.2), so we consider this equivalence to be one of our primary contributions.
中文: 我们利用这种参数化(第4.2节)获得了最佳的样本质量结果,因此我们认为这种等同性是我们的主要贡献之一。
<a id="S0017"></a> Source: p.2 S0017
Original: Despite their sample quality, our models do not have competitive log likelihoods compared to other likelihood-based models (our models do, however, have log likelihoods better than the large estimates annealed importance sampling has been reported to produce for energy based models and score matching [11, 55]).
中文: 尽管样本质量较高,但与其他基于可能性的模型相比,我们的模型没有竞争性的日志可能性(然而,我们的模型的确比大型估算的无记名重要性抽样更有可能为基于能源的模型和比分[11、55])。
<a id="S0018"></a> Source: p.2 S0018
Original: We find that the majority of our models’ lossless codelengths are consumed to describe imperceptible image details (Section 4.3).
中文: 我们发现,我们模型的大部分无损码长都用来描述无法察觉的图像细节(第4.3节)。
<a id="S0019"></a> Source: p.2 S0019
Original: We present a more refined analysis of this phenomenon in the language of lossy compression, and we show that the sampling procedure of diffusion models is a type of progressive decoding that resembles autoregressive decoding along a bit ordering that vastly generalizes what is normally possible with autoregressive models. 2 Background (cid:82) Diffusion models [53] are latent variable models of the form p (x ) := p (x ) dx , where θ 0 θ 0:T 1:T x , . . . , x are latents of the same dimensionality as the data x q(x ).
中文: 我们用失落压缩的语言提出了对这一现象的更精细的分析,我们显示,扩散模型的取样程序是一种渐进的解码方法,它类似于沿着一点点顺序的自递分解,它大大概括了通常情况下用自递分解模型可以做到的事情。 2 背景(cid:82) 扩散模型 [53] 是形式 p (x):= p (x) dx 的潜伏可变模型,其中 0 θ 0: T 1: T x.,., x 是与数据 x q (x) 相同的维度的潜伏.
<a id="S0020"></a> Source: p.2 S0020
Original: The joint distribution 1 T 0 0 ∼ p (x ) is called the reverse process, and it is defined as a Markov chain with learned Gaussian θ 0:T transitions starting at p(x ) = (x ; 0, I): T T N T (cid:89) p (x ) := p(x ) p (x x ), p (x x ) := (x ; µ (x , t), Σ (x , t)) (1) θ 0:T T θ t − 1 | t θ t − 1 | t N t − 1 θ t θ t t=1 What distinguishes diffusion models from other types of latent variable models is that the approximate posterior q(x x ), called the forward process or diffusion process, is fixed to a Markov chain that 1:T 0 | gradually adds Gaussian noise to the data according to a variance schedule β , . . . , β : 1 T T (cid:89) (cid:112) q(x x ) := q(x x ), q(x x ) := (x ; 1 β x , β I) (2) 1:T 0 t t 1 t t 1 t t t 1 t | | − | − N − − t=1 Training is performed by optimizing the usual variational bound on negative log likelihood: (cid:20) (cid:21) (cid:20) (cid:21) E [ log p θ (x 0 )] E q log p θ (x 0:T ) = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) =: L (3) − ≤ − q(x x ) − − q(x x ) 1:T 0 t t 1 | t 1 | − ≥ The forward process variances β can be learned by reparameterization [33] or held constant as t hyperparameters, and expressiveness of the reverse process is ensured in part by the choice of Gaussian conditionals in p (x x ), because both processes have the same functional form when θ t 1 t β are small [53]. A notable p−ro | perty of the forward process is that it admits sampling x at an t t arbitrary timestep t in closed form: using the notation α := 1 β and α¯ := (cid:81)t α , we have t − t t s=1 s q(x x ) = (x ; √α¯ x , (1 α¯ )I) (4) t 0 t t 0 t | N − 2
中文: 联合分布 1 T 0 ∼ p (x) 被称作倒转过程,它被定义为有学识的高斯克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克克 扩散模型与其他类型的潜在可变模型的区别在于,称为前向过程或扩散过程的近似后方的q(xx)被固定在一个马可夫链上,即: 1:T 0-Q|会根据差异表β,.逐渐将高斯噪音添加到数据中. , β: 1 T (cid:89)(cid:112) q (xx): = q (xx), q (xxx): = (x; 1 β x, β I) (2) 1: T 0 t 1 t 1 t 1 t 1 t 1 t 1 t 1 t 1 t = L (3) = = (cid:20) (cid:20) (cid:20) (cid:21) (cid:21) (cid:21) = E [log p → (x)] E q → (x: T) = E q → (cid:88) log (x-t--------------------------------------------------------------------------------------------- 前向过程差异β可以通过再参数化[33]或以t高参数保持常数来学习,反向过程的表达性部分通过p (xx)中高斯条件的选择来保证,因为当-t 1tβ为小[53]时,这两个过程具有相同的功能形式. 向前过程的一个显著的p-ro-| perty是它以封闭的形式在t t 任意的时步t 上接受采样x:使用注解 α:= 1 β和 α':= (cid:81)t α,我们有 t- t s= 1 s q(x) → (x; √α, (1 α) I) (4) t 0 t → 2
<a id="S0021"></a> Source: p.3 S0021
Original: Efficient training is therefore possible by optimizing random terms of L with stochastic gradient descent.
中文: 因此,通过优化L的随机条件和有花样的梯度下降,可以进行有效的培训。
<a id="S0022"></a> Source: p.3 S0022
Original: Further improvements come from variance reduction by rewriting L (3) as: (cid:20) (cid:21) (cid:88) E D (q(x x ) p(x )) + D (q(x x , x ) p (x x )) log p (x x ) (5) q KL T 0 T KL t 1 t 0 θ t 1 t θ 0 1 (cid:124) | (cid:123)(cid:122) (cid:107) (cid:125) (cid:124) − | (cid:123)(cid:122) (cid:107) − | (cid:125) − (cid:124) (cid:123)(cid:122) | (cid:125) t>1 LT Lt 1 L0 − (See Appendix A for details.
中文: 进一步的改进来自通过将L(3)改写为:(cid:20)(cid:21)(cid:88) E D (q(xx)) p (xx) + D (q(xxx,xx) p (xxx)) log p (xx) (5) q KL T 0 T KL T 1 t 0 T 1 t → 1 (cid:124) → (cid:123)(cid:107)(cid:124) → → (cid:123)(cid:107)(cid:122)(cid:125)(cid:124)(cid:123)(cid:123)(cid:122) → (cid:125) → (cid:125)(cid:1222) → (cid:125) T (cid:1) LT 1 LT 1 L0 → (cid:107)(见附录) - 详细情况 A.
<a id="S0023"></a> Source: p.3 S0023
Original: The labels on the terms are used in Section 3.) Equation (5) uses KL divergence to directly compare p (x x ) against forward process posteriors, which are tractable θ t 1 t when conditioned on x : − | 0 q(x x , x ) = (x ; µ˜ (x , x ), β˜ I), (6) t − 1 | t 0 N t − 1 t t 0 t √α¯ β √α (1 α¯ ) 1 α¯ where µ˜ t (x t , x 0 ) := 1 t − α¯ 1 t x 0 + t 1 − α¯ t − 1 x t and β˜ t := 1 − α¯ t − 1 β t (7) t t t − − − Consequently, all KL divergences in Eq. (5) are comparisons between Gaussians, so they can be calculated in a Rao-Blackwellized fashion with closed form expressions instead of high variance Monte Carlo estimates. 3 Diffusion models and denoising autoencoders Diffusion models might appear to be a restricted class of latent variable models, but they allow a large number of degrees of freedom in implementation.
中文: 第3节使用了术语上的标签。 ) (5)利用KL相差来直接比较p(xx)与前方过程后缀相差,当以x===================================================================================================;=================================;==============================;========================;======================================= 3 扩散模型和去诺自编码器 扩散模型可能似乎是潜在可变模型的有限类别,但它们允许大量自由实施。
<a id="S0024"></a> Source: p.3 S0024
Original: One must choose the variances β of the t forward process and the model architecture and Gaussian distribution parameterization of the reverse process.
中文: 人们必须选择 t 前进过程的差异 β 和 模式架构 和 高斯分配参数化 逆向过程 .
<a id="S0025"></a> Source: p.3 S0025
Original: To guide our choices, we establish a new explicit connection between diffusion models and denoising score matching (Section 3.2) that leads to a simplified, weighted variational bound objective for diffusion models (Section 3.4).
中文: 为了指导我们的选择,我们在扩散模型和去名分比(第3.2节)之间建立了新的明确联系,从而形成一个简化的、加权的可变约束的传播模型目标(第3.4节)。
<a id="S0026"></a> Source: p.3 S0026
Original: Ultimately, our model design is justified by simplicity and empirical results (Section 4).
中文: 归根结底,我们的模型设计以简单和实证结果为依据(第4节)。
<a id="S0027"></a> Source: p.3 S0027
Original: Our discussion is categorized by the terms of Eq. (5). 3.1 Forward process and L T We ignore the fact that the forward process variances β are learnable by reparameterization and t instead fix them to constants (see Section 4 for details).
中文: 我们的讨论按照Eq. (5)的规定分类。 3.1 前进过程和L T 我们忽略了这样一个事实,即前进过程差异β可以通过重新参数化来学习,而将其固定为常数(详情见第4节)。
<a id="S0028"></a> Source: p.3 S0028
Original: Thus, in our implementation, the approximate posterior q has no learnable parameters, so L is a constant during training and can be ignored. T 3.2 Reverse process and L 1:T 1 − Now we discuss our choices in p (x x ) = (x ; µ (x , t), Σ (x , t)) for 1 < t T .
中文: 因此,在我们的执行中,大概的后q没有可学习的参数,因此L是训练期间的常数,可以忽略. T 3.2 倒置过程和L 1:T 1 − 现在我们以 p (x x) = (x; μ (x, t), Σ (x, t) 来讨论我们的选择 1 < t T.
<a id="S0029"></a> Source: p.3 S0029
Original: First, we set Σ (x , t) = σ2I to untrain θ ed t t−im 1 | e d t epen N dent t −co 1 nst θ ants t .
中文: 首先,我们设置了"(x,t)"="σ"2I去去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"去"""""""""""""""""""""""""""
<a id="S0030"></a> Source: p.3 S0030
Original: Expe θ rim t entally, both σ2≤ = β and θ t t t t σ se t 2 co = nd β˜ t is = op 1 ti − 1 m− α¯ a α t ¯− l t 1 fo β r t x had d s e i t m er i m la i r n r is e t s i u c l a t l s l . y T se h t e t fi o rs o t n c e h p o o ic in e t. is T o h p e ti s m e a a l re fo t r h x e 0 tw ∼ o N ex ( t 0 re , m I) e , c a h n o d ic th e e s 0 corresponding to upper and lower bounds on reverse process entropy for data with coordinatewise unit variance [53].
中文: θ θ β β β β β β β β β β β β β β β β β β β β β β β ̄− ̄− ̄− 1ti 1m 1 fo 1 fo 1 fo 1 fo 1β 1β 1β 1β 1β 1β 1β e 1β 1β 1 e 1 e 1 e 1 e 1 e 1 e 1 s 1 s 1 s 1 s 1 s 1 s 1 s 1 s 1 s 1 s e 1 s 1 s e 1 s 1 s e 1 s 1 s 1 s 1 s 1 s 1 s 1 s 1 s s 1 s corresponding 1 s s 1 s 1 s 1 s 1 and 1 and 1 and corresponding 1 s 1 and 1 s 1 s corresponding corresponding corresponding 1s corresponding 1s 1s 1s 1s 1s 1s 1s upper 1s upper 1s 1s upper 1s 1s 1s 1s 1s 1s 1s upper 1s upper 1s 1s upper 1s 1s 1s bound 1s bound
<a id="S0031"></a> Source: p.3 S0031
Original: Second, to represent the mean µ (x , t), we propose a specific parameterization motivated by the θ t following analysis of L .
中文: 第二,为了代表平均值μ (x,t),我们提议在L 分析之后,以 \ t 为动机进行具体参数化。
<a id="S0032"></a> Source: p.3 S0032
Original: With p (x x ) = (x ; µ (x , t), σ2I), we can write: t θ t − 1 | t N t − 1 θ t t (cid:20) (cid:21) 1 L = E µ˜ (x , x ) µ (x , t) 2 + C (8) t − 1 q 2σ t 2 (cid:107) t t 0 − θ t (cid:107) where C is a constant that does not depend on θ.
中文: 有p (x x) = (x; μ (x, t), \ 2I) 等,我们可以写出: t → 1 → (x, t) → (cid: 20) (cid: 21) 1 L = E μ → (x, t) 2 + C (8) t → 1 q 2 → (cid: 107) t → (cid: 107) C 是一个不依赖于 → (x, t) 的常数.
<a id="S0033"></a> Source: p.3 S0033
Original: So, we see that the most straightforward parameterization of µ is a model that predicts µ˜ , the forward process posterior mean.
中文: 因此,我们看到,μ最直接的参数化是一个预测μ的模型,即后期过程的意思.
<a id="S0034"></a> Source: p.3 S0034
Original: However, we can expand θ t Eq. (8) further by reparameterizing Eq. (4) as x (x , (cid:15)) = √α¯ x + √1 α¯ (cid:15) for (cid:15) (0, I) and t 0 t 0 t − ∼ N applying the forward process posterior formula (7): (cid:34) (cid:13) (cid:18) (cid:19) (cid:13)2 (cid:35) L t − 1 − C = E x0,(cid:15) 2σ 1 t 2 (cid:13) (cid:13) (cid:13) µ˜ t x t (x 0 , (cid:15)), √ 1 α¯ t (x t (x 0 , (cid:15)) − √1 − α¯ t (cid:15)) − µ θ (x t (x 0 , (cid:15)), t) (cid:13) (cid:13) (cid:13) (9) (cid:34) (cid:13) (cid:18) (cid:19) (cid:13)2 (cid:35) = E x0,(cid:15) 2σ 1 2 (cid:13) (cid:13) (cid:13) √ 1 α x t (x 0 , (cid:15)) − √1 β t α¯ (cid:15) − µ θ (x t (x 0 , (cid:15)), t) (cid:13) (cid:13) (cid:13) (10) t t − t 3
中文: 然而,我们可以进一步扩展 α t Eq. (8) 通过将 Eq. (4) 重新校正为 x (x, (cid:15) = → (x, (cid:15) → (cid:15) 为 (cid:15) (0, I) 和 t 0 t 0 t- → N 应用前进过程后方公式 (7) : (cid:34) (cid:13) (cid:18) (cid:19) (cid:13) Lt → 1 → C= Ex0 (cid:15) 2 – (cid:13) (cid:13) (cid:13) (cid:13) (cid:13-d:13) (cid:13-d:13) (cid:13) (cid:13:cid:13) (cid:13:cid:11-d:13) (cid:13) (cid:13) (cid:11-d:13) (cid:13) (cid:13) (cid:13
<a id="S0035"></a> Source: p.4 S0035
Original: Algorithm 1 Training Algorithm 2 Sampling 1: repeat 1: x ∼ N (0, I) T 2: x ∼ q(x ) 0 0 2: for t = T, . . . , 1 do 3: t ∼ Uniform({1, . . . , T }) 3: z ∼ N (0, I) if t > 1, else z = 0 4: (cid:15) ∼ N (0, I) (cid:16) (cid:17) 5: Take ∇ g θ ra (cid:13) (cid:13) d (cid:15) ie − nt (cid:15) d θ e ( s √ ce α¯ n t t x s 0 te + p o √ n 1 − α¯ t (cid:15), t) (cid:13) (cid:13) 2 4 5 : : en x d t− f 1 or = √1 αt x t − √1 1 − − α α¯ t t (cid:15) θ (x t , t) + σ t z 6: until converged 6: return x 0 (cid:16) (cid:17) Equation (10) reveals that µ must predict 1 x βt (cid:15) given x .
中文: 算法 1 训练 算法 2 抽样 1 重复 1: x ∼ N (0, I) T 2: x ∼ q (x) 0 2: 为 t = T,., 1 do 3 : t { 1,., T } 3 : z ∼ N (0, I) 如 > 1, 或 z = 0 4 : (cid:15) ∼ N (0, I) (cid:16) (cid:17) 5 : 取出 ∇克 ra (cid:13) d (cid:13) i − (cid:15) d e (cid:15) dθ e ( s√ √ √ ̄ ̄ ̄ ̄ ̄ ̄ ̄ ̄ x − − − √ (x :15: 1μ- (10); (10) (10) (10); (10); (10); (10); (10); (10); 13); (10); (10); 13); 13); 13); 13);
<a id="S0036"></a> Source: p.4 S0036
Original: Since x is available as input to the model, we may c θ hoose the param √ e α t t eriza t ti − on √1 − α¯t t t (cid:18) (cid:19) (cid:18) (cid:19) 1 1 β µ (x , t) = µ˜ x , (x √1 α¯ (cid:15) (x )) = x t (cid:15) (x , t) (11) θ t t t √α¯ t − − t θ t √α t − √1 α¯ θ t t t t − where (cid:15) is a function approximator intended to predict (cid:15) from x .
中文: 由于 x 可以作为模型的输入,我们可以将 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
<a id="S0037"></a> Source: p.4 S0037
Original: To sample x p (x x ) is θ t t 1 θ t 1 t (cid:16) (cid:17) − ∼ − | to compute x = 1 x βt (cid:15) (x , t) + σ z, where z (0, I).
中文: 取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取取
<a id="S0038"></a> Source: p.4 S0038
Original: The complete sampling procedure, A t l − g 1 orith √ m αt 2, re t se − m √ bl 1 e−s α¯ L t an θ gev t in dynam t ics with (cid:15) ∼ a N s a learned gradient of the data θ density.
中文: 完整的取样程序,A t − g 1 → m αt 2, ret se- m → bl 1 e-s → s → 在 dynam t ics中用 (cid:15) a N 表示数据密度的已学习梯度。
<a id="S0039"></a> Source: p.4 S0039
Original: Furthermore, with the parameterization (11), Eq. (10) simplifies to: E x0,(cid:15) (cid:20) 2σ2α β (1 t 2 α¯ ) (cid:13) (cid:13)(cid:15) − (cid:15) θ (√α¯ t x 0 + √1 − α¯ t (cid:15), t) (cid:13) (cid:13) 2 (cid:21) (12) t t − t which resembles denoising score matching over multiple noise scales indexed by t [55].
中文: 此外,随着参数化(11),Eq.(10)简化为:E x0(cid:15) (cid:20) 2/3/2α β (1t 2 α ̄ (cid:13) (cid:13) (cid:15) − (cid:15) → (X't x 0 + √ 1 → t (cid:15)),t (cid:13) 2 (cid:21) (12) t - t 类似于以t [55] 索引的多噪分尺上的去诺比分.
<a id="S0040"></a> Source: p.4 S0040
Original: As Eq. (12) is equal to (one term of) the variational bound for the Langevin-like reverse process (11), we see that optimizing an objective resembling denoising score matching is equivalent to using variational inference to fit the finite-time marginal of a sampling chain resembling Langevin dynamics.
中文: 由于Eq.(12)等于(一个术语)Langevin类似倒置过程的变异性约束(11),我们看到,优化一个类似去诺能分数匹配的目标相当于使用变异推论来适应一个类似Langevin动态的抽样链的有限时间边际.
<a id="S0041"></a> Source: p.4 S0041
Original: To summarize, we can train the reverse process mean function approximator µ to predict µ˜ , or by θ t modifying its parameterization, we can train it to predict (cid:15). (There is also the possibility of predicting x , but we found this to lead to worse sample quality early in our experiments.) We have shown that 0 the (cid:15)-prediction parameterization both resembles Langevin dynamics and simplifies the diffusion model’s variational bound to an objective that resembles denoising score matching.
中文: 概括地说,我们可以训练反向过程指函数近似于μ来预测μ QQ,或者通过 \ t修改其参数化,我们可以训练它来预测(cid:15). (还有预测x的可能性,但我们发现这会导致实验初期样本质量更差. ) 也简化了扩散模型的变异性,
<a id="S0042"></a> Source: p.4 S0042
Original: Nonetheless, it is just another parameterization of p (x x ), so we verify its effectiveness in Section 4 in an θ t 1 t ablation where we compare predicting (cid:15) aga−in | st predicting µ˜ . t 3.3 Data scaling, reverse process decoder, and L 0 We assume that image data consists of integers in 0, 1, . . . , 255 scaled linearly to [ 1, 1].
中文: 然而,它只是p (x x) 的又一参数化,所以我们在第4节中验证它的有效性,用一个't 1 t' ablusion来比较我们预测 (cid:15) aga-in → st 预测 μ. t 3.3 数据缩放 逆向过程解码器 L 0 我们假设图像数据由整数组成,以 0, 1,., 255线性缩放为 [ 1, 1].
<a id="S0043"></a> Source: p.4 S0043
Original: This { } − ensures that the neural network reverse process operates on consistently scaled inputs starting from the standard normal prior p(x ).
中文: 此 { } - 确保神经网络反向过程从标准正常的p( x) 开始, 运行在一致的缩放输入上 。
<a id="S0044"></a> Source: p.4 S0044
Original: To obtain discrete log likelihoods, we set the last term of the reverse T process to an independent discrete decoder derived from the Gaussian (x ; µ (x , 1), σ2I): N 0 θ 1 1 (cid:89) D (cid:90) δ+(xi 0 ) p (x x ) = (x; µi (x , 1), σ2) dx θ 0 | 1 N θ 1 1 i=1 δ − (xi 0 ) (13) (cid:26) (cid:26) if x = 1 if x = 1 δ (x) = ∞ δ (x) = −∞ − + x + 1 if x < 1 − x 1 if x > 1 255 − 255 − where D is the data dimensionality and the i superscript indicates extraction of one coordinate. (It would be straightforward to instead incorporate a more powerful decoder like a conditional autoregressive model, but we leave that to future work.) Similar to the discretized continuous distributions used in VAE decoders and autoregressive models [34, 52], our choice here ensures that the variational bound is a lossless codelength of discrete data, without need of adding noise to the data or incorporating the Jacobian of the scaling operation into the log likelihood.
中文: 为了获得离散的日志可能性,我们将倒转 T 过程的最后一个术语设定为由高斯琴衍生出的独立离散解码器(x; μ (x, 1), ç : 2I): N 0 → 1 (cid:89) D (cid:90) → (x) p (x (x; μi (x, 1), σ 2) dx → 0 → 1 N → 1 → (x (x; 1) (cid:26) (cid:26) 如果x = 1 → (x) → (x) = 1 → + + + + 1 如果x → 1 如果x > 1 → 1 → 1 如果 1 → 1 255 - 数据维度, i 上标显示提取一个坐标 。 (将一个更强大的解码器像一个有条件的自递模式,是直截了当的,但我们把它留给今后的工作。 ) 与VAE解码器和自递回式模型[34,52]中使用的光碟化连续分布类似,我们在这里的选择确保了变异绑定是离散数据的无损码长,不需要给数据添加噪音,也不需要将缩放操作的雅各比人纳入日志可能性.
<a id="S0045"></a> Source: p.4 S0045
Original: At the end of sampling, we display µ (x , 1) noiselessly. θ 1 3.4 Simplified training objective With the reverse process and decoder defined above, the variational bound, consisting of terms derived from Eqs. (12) and (13), is clearly differentiable with respect to θ and is ready to be employed for 4
中文: 在取样结束时,我们无声显示μ (x, 1). θ 1 3.4 简化训练目标 以上文定义的倒置过程和解码器,由Eqs.(12)和(13)等术语组成的变异约束显然与 θ不同,并准备用于4个
<a id="S0046"></a> Source: p.5 S0046
Original: Model IS FID NLL Test (Train) Table 2: Unconditional CIFAR10 reverse Conditional process parameterization and training objec- EBM [11] 8.30 37.9 tive ablation.
中文: Model IS FID NLL Test (Train) 表2:无条件 CIFAR10逆向条件工艺参数化和训练 objec-EBM [11] 8.30 37.9 型机车减速.
<a id="S0047"></a> Source: p.5 S0047
Original: Blank entries were unstable to JEM [17] 8.76 38.4 train and generated poor samples with out-of- BigGAN [3] 9.22 14.73 range scores.
中文: 空白条目对正义运动来说是不稳定的 [17] 8.76 38.4 列车,并以出局BigGAN[3] 9.22 14.73 射程分数产生差的样本.
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Original: StyleGAN2 + ADA (v1) [29] 10.06 2.67 Objective IS FID Unconditional µ˜ prediction (baseline) Diffusion (original) [53] 5.40 Gated PixelCNN [59] 4.60 65.93 3.0 ≤ 3 (2.90) L, learned diagonal Σ 7.28 0.10 23.69 Sparse Transformer [7] 2.80 L, fixed isotropic Σ 8.06 ± 0.09 13.22 PixelIQN [43] 5.29 49.46 µ˜ µ˜ 2 ± – – EBM [11] 6.78 38.2 (cid:107) − θ(cid:107) NCSNv2 [56] 31.75 (cid:15) prediction (ours) NCSN [55] 8.87 0.12 25.32 SNGAN [39] 8.22 ± 0.05 21.7 L, learned diagonal Σ – – S S N ty G le A G N A - N D 2 D + L A S D [4 A ] (v1) [29] 9 9 . . 7 0 4 9 ± ± 0 0 . . 1 0 0 5 1 3 5 . . 2 4 6 2 (cid:107) L ˜(cid:15) , fi − xe (cid:15) d θ i (cid:107) so 2 tr ( o L p s ic im Σ ple) 9 7 . . 4 6 6 7 ± ± 0 0. . 1 1 3 1 1 3 3 . . 1 5 7 1 Ours (L, fixed isotropic Σ) 7.67 ± 0.13 13.51 3.70 (3.69) Ours (Lsimple) 9.46 ± ± 0.11 3.17 ≤ ≤ 3.75 (3.72) training.
中文: StyleGAN2 + ADA (v1) [29] 10.06 2.67 目标 IS FID 无条件 μ → → 预测 (底线) Difusion (原作) [53] 5.40 Gated PixelCNN [59] 4.60 65.93 3.0 → 3 (2.90) L, 学习对等分数 → 7.28 0.10 23.69 Sparse 变形器 [7] 2.80 L, 固定同分数 → 13.09 → 13.22 PixelIQN [43] 49.46 μ → → → → → → → → → EBM [11] 6.78 3.3 (cid:107) NCSNSNv2 [56] → → 31.75 L (cid. 1 (3 ± ± + − 3° 1 + 1 + + 1 − ° 1 ° 1 ° 1 ° 1 ° 1 ° 1 = 0° 1 = 0° 1 = 0° 1° = 0°
<a id="S0049"></a> Source: p.5 S0049
Original: However, we found it beneficial to sample quality (and simpler to implement) to train on the following variant of the variational bound: L simple (θ) := E t,x0,(cid:15) (cid:104)(cid:13) (cid:13)(cid:15) − (cid:15) θ (√α¯ t x 0 + √1 − α¯ t (cid:15), t) (cid:13) (cid:13) 2 (cid:105) (14) where t is uniform between 1 and T .
中文: 然而,我们发现在变异绑定的下列变体上进行试样质量(并且执行起来更简单)的训练是有好处的: L 简单 (θ):= E t,x0, (cid:15) (cid:104 (cid:13) (cid:13) (cid:15)- (cid:15) → (√α t + 0 + √ 1) → (cid:15) (cid:13) (cid:13) 2 (cid:105) (14),其中t在1到T之间是统一的.
<a id="S0050"></a> Source: p.5 S0050
Original: The t = 1 case corresponds to L with the integral in the 0 discrete decoder definition (13) approximated by the Gaussian probability density function times the bin width, ignoring σ2 and edge effects.
中文: t = 1 大小写对应 L ,在 0 离散分解码器定义中包含组件 (13),与高斯概率密度函数乘以 bin 宽度相近,忽略了 ç2 和边缘效果.
<a id="S0051"></a> Source: p.5 S0051
Original: The t > 1 cases correspond to an unweighted version of 1 Eq. (12), analogous to the loss weighting used by the NCSN denoising score matching model [55]. (L does not appear because the forward process variances β are fixed.) Algorithm 1 displays the T t complete training procedure with this simplified objective.
中文: t > 1个案例对应了1 Eq. (12)的未加权版本,类似于NCSN去诺比分比对模型使用的减重. [55]. (L不出现,因为前方流程差异β是固定的。 ) 算法 1 显示带有这个简化目标的 T t 完整的训练程序.
<a id="S0052"></a> Source: p.5 S0052
Original: Since our simplified objective (14) discards the weighting in Eq. (12), it is a weighted variational bound that emphasizes different aspects of reconstruction compared to the standard variational bound [18, 22].
中文: 由于我们的简化目标(14)放弃了Eq.(12)中的权重,它是一种加权变异约束,它强调重建的不同方面,而标准变异约束[18,22].
<a id="S0053"></a> Source: p.5 S0053
Original: In particular, our diffusion process setup in Section 4 causes the simplified objective to down-weight loss terms corresponding to small t.
中文: 特别是,我们在第4节设定的传播过程导致简化目标,即降低重量的损失条件相当于小吨。
<a id="S0054"></a> Source: p.5 S0054
Original: These terms train the network to denoise data with very small amounts of noise, so it is beneficial to down-weight them so that the network can focus on more difficult denoising tasks at larger t terms.
中文: 这些名词训练网络以极小的噪音来去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去去
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Original: We will see in our experiments that this reweighting leads to better sample quality. 4 Experiments We set T = 1000 for all experiments so that the number of neural network evaluations needed during sampling matches previous work [53, 55].
中文: 我们会在实验中看到,这种再加权会导致更好的样本质量. 4个实验 我们为所有实验设定 T = 1000,这样在取样时所需的神经网络评价数量与以前的工作相匹配 [53, 55].
<a id="S0056"></a> Source: p.5 S0056
Original: We set the forward process variances to constants increasing linearly from β = 10 4 to β = 0.02.
中文: 我们设定了前进过程差异,使β = 10 4 到β = 0.02的常数线性增长。
<a id="S0057"></a> Source: p.5 S0057
Original: These constants were chosen to be small 1 − T relative to data scaled to [ 1, 1], ensuring that reverse and forward processes have approximately − the same functional form while keeping the signal-to-noise ratio at x as small as possible (L = T T D (q(x x ) (0, I)) 10 5 bits per dimension in our experiments).
中文: 这些常数被选为小 1 - T 相对于被缩放为 [1, 1] 的数据,确保倒向和前向过程的功能形式大致相同,同时将信号-噪声比尽可能小(L = T T D (q (x x) (0, I)) 10个比特,在我们实验中每个维度.
<a id="S0058"></a> Source: p.5 S0058
Original: KL T 0 − | (cid:107) N ≈ To represent the reverse process, we use a U-Net backbone similar to an unmasked PixelCNN++ [52, 48] with group normalization throughout [66].
中文: KL T 0 – | (cid:107) N ≈ 为代表倒转过程,我们使用一个U-Net主干线,类似于一个未被遮盖的PixelCNN++ [52,48],整个[66] 实现团体正常化.
<a id="S0059"></a> Source: p.5 S0059
Original: Parameters are shared across time, which is specified to the network using the Transformer sinusoidal position embedding [60].
中文: 参数是跨时间共享的,使用嵌入式变形器 sinusoidal 位置向网络指定 [60].
<a id="S0060"></a> Source: p.5 S0060
Original: We use self-attention at the 16 16 feature map resolution [63, 60].
中文: 我们在16个16个地物地图分辨率[63,60]上使用自觉.
<a id="S0061"></a> Source: p.5 S0061
Original: Details are in Appendix B. × 4.1 Sample quality Table 1 shows Inception scores, FID scores, and negative log likelihoods (lossless codelengths) on CIFAR10.
中文: 详情见附录B×4.1。 样本质量表1显示CIFAR10上的受试分数,FID分数,和负对数概率(无损失码长).
<a id="S0062"></a> Source: p.5 S0062
Original: With our FID score of 3.17, our unconditional model achieves better sample quality than most models in the literature, including class conditional models.
中文: 随着我们的FID分数为3.17,我们的无条件模型比文献中大多数模型,包括类有条件模型,都取得了更好的样本质量.
<a id="S0063"></a> Source: p.5 S0063
Original: Our FID score is computed with respect to the training set, as is standard practice; when we compute it with respect to the test set, the score is 5.24, which is still better than many of the training set FID scores in the literature. 5
中文: 我们的FID分数是根据培训集的标准做法计算的;当我们计算测试集时,得分是5.24分,这仍然比文献中许多培训集的FID分数要好. 页:1
<a id="S0064"></a> Source: p.6 S0064
Original: FID=7.89 Figure 4: LSUN Bedroom samples.
中文: FID=7.89 图4:LSUN卧室样本.
<a id="S0065"></a> Source: p.6 S0065
Original: FID=4.90 Algorithm 3 Sending x Algorithm 4 Receiving 0 1: Send x T ∼ q(x T |x 0 ) using p(x T ) 1: Receive x T using p(x T ) 2: for t = T − 1, . . . , 2, 1 do 2: for t = T − 1, . . . , 1, 0 do 3: Send x t ∼ q(x t |x t+1 , x 0 ) using p θ (x t |x t+1 ) 3: Receive x t using p θ (x t |x t+1 ) 4: end for 4: end for 5: Send x 0 using p θ (x 0 |x 1 ) 5: return x 0 We find that training our models on the true variational bound yields better codelengths than training on the simplified objective, as expected, but the latter yields the best sample quality.
中文: FID=4.90 算法 3 发送x算法 4 接收0 1: 发送x T ∼ (x T | (x T |) 使用p (x T) 1: 接收x T 使用p (x T) 2: 为t = T - 1,., 2, 1 do 2 : 为t = T − 1,., 1, 0 do 3 : 发送x t q (x | (x |) + 1, x 0 ) 使用p → (x) 3 : 接收x t 使用p → (x) → (x) +1) 4 : 结束为 5: 发送x 0 使用p → (x 0 |x 1) 5 : 返回x 0 : 我们发现, 培训我们真正变异约束的模型的代码长度比对简化目标的培训要好, 但后者的样本质量最好。
<a id="S0066"></a> Source: p.6 S0066
Original: See Fig. 1 for CIFAR10 and CelebA-HQ 256 256 samples, Fig. 3 and Fig. 4 for LSUN 256 256 samples [71], × × and Appendix D for more. 4.2 Reverse process parameterization and training objective ablation In Table 2, we show the sample quality effects of reverse process parameterizations and training objectives (Section 3.2).
中文: 关于CIFAR10和CelebA-HQ256样本,请参见图1;关于LSUN256-256样本,请参见图3和图4[71]、x和附录D。 4.2 逆向进程参数化和培训目标化 在表2中,我们显示逆向进程参数化和培训目标的样本质量影响(第3.2节)。
<a id="S0067"></a> Source: p.6 S0067
Original: We find that the baseline option of predicting µ˜ works well only when trained on the true variational bound instead of unweighted mean squared error, a simplified objective akin to Eq. (14).
中文: 我们发现,只有当接受过关于真正的可变约束而不是未加权平均平方误差的培训时,预测μ-Q的基线选择才有效,这个简化目标类似于Eq.(14)。
<a id="S0068"></a> Source: p.6 S0068
Original: We also see that learning reverse process variances (by incorporating a parameterized diagonal Σ (x ) into the variational bound) leads to unstable training and poorer sample quality θ t compared to fixed variances.
中文: 我们还看到,学习逆向过程差异(将参数化的对角(x)纳入变量约束)导致培训不稳定,与固定差异相比样本质量更差。
<a id="S0069"></a> Source: p.6 S0069
Original: Predicting (cid:15), as we proposed, performs approximately as well as predicting µ˜ when trained on the variational bound with fixed variances, but much better when trained with our simplified objective. 4.3 Progressive coding Table 1 also shows the codelengths of our CIFAR10 models.
中文: 正如我们所建议的那样,预测(cid:15)在接受关于固定差异的变异性培训时,表现大致和预测微分,但在接受关于我们简化目标的培训时,表现要好得多。 4.3 渐进编码表1还显示了我国CIFAR10型机车的编码长度。
<a id="S0070"></a> Source: p.6 S0070
Original: The gap between train and test is at most 0.03 bits per dimension, which is comparable to the gaps reported with other likelihood-based models and indicates that our diffusion model is not overfitting (see Appendix D for nearest neighbor visualizations).
中文: 列车与测试间的差距为每个维度最多0.03比特,这与其他基于概率的模型所报告的差距相上下,并表明我们的传播模型并不过于相配(最近的相邻可视化功能见附录D).
<a id="S0071"></a> Source: p.6 S0071
Original: Still, while our lossless codelengths are better than the large estimates reported for energy based models and score matching using annealed importance sampling [11], they are not competitive with other types of likelihood-based generative models [7].
中文: 然而,虽然我们的无损失编码长度优于关于基于能源的模型的大规模估计,并使用无记忆重要性取样法进行比对[11],但它们与其他类型的基于概率的基因模型没有竞争力[7]。
<a id="S0072"></a> Source: p.6 S0072
Original: Since our samples are nonetheless of high quality, we conclude that diffusion models have an inductive bias that makes them excellent lossy compressors.
中文: 由于我们的样品质量很高,我们得出结论,扩散模型具有诱导性偏差,使它们成为极佳的失落压缩器.
<a id="S0073"></a> Source: p.6 S0073
Original: Treating the variational bound terms L + + L 1 T · · · as rate and L as distortion, our CIFAR10 model with the highest quality samples has a rate of 1.78 0 bits/dim and a distortion of 1.97 bits/dim, which amounts to a root mean squared error of 0.95 on a scale from 0 to 255.
中文: 将变异约束术语L + + L 1 T + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
<a id="S0074"></a> Source: p.6 S0074
Original: More than half of the lossless codelength describes imperceptible distortions.
中文: 超过半数的无损码长描述出无法察觉的扭曲.
<a id="S0075"></a> Source: p.6 S0075
Original: Progressive lossy compression We can probe further into the rate-distortion behavior of our model by introducing a progressive lossy code that mirrors the form of Eq. (5): see Algorithms 3 and 4, which assume access to a procedure, such as minimal random coding [19, 20], that can transmit a sample x q(x) using approximately D (q(x) p(x)) bits on average for any distributions p and KL ∼ (cid:107) q, for which only p is available to the receiver beforehand.
中文: 逐渐丢失压缩 我们可以进一步探究我们模型的速率扭曲行为,方法是引入一个反映 Eq. (5) 形式的渐进式丢失代码:见算法 第3和第4条,它假定可以访问一个程序,例如最小随机编码[19, 20], 它可以使用任何分布p 和 KL (cid:107) q 平均大约 D (q (x) p (x) 位来传输一个样本 x q (x) , 而接收器在此之前只能使用 p .
<a id="S0076"></a> Source: p.6 S0076
Original: When applied to x q(x ), Algorithms 3 0 0 ∼ and 4 transmit x , . . . , x in sequence using a total expected codelength equal to Eq. (5).
中文: 当应用到 x q (x) 时, 算法为 3 0 0 − 和 4 传送 x ,. x 以等于 Eq. (5) 的总预期码长为序.
<a id="S0077"></a> Source: p.7 S0077
Original: at any time t, has the partial information x fully available and can progressively estimate: t (cid:0) (cid:1) x xˆ = x √1 α¯ (cid:15) (x ) /√α¯ (15) 0 0 t t θ t t ≈ − − due to Eq. (4). (A stochastic reconstruction x p (x x ) is also valid, but we do not consider 0 θ 0 t ∼ | it here because it makes distortion more difficult to evaluate.) Figure 5 shows the resulting ratedistortion plot on the CIFAR10 test set.
中文: 在任何时间,有完全可用的部分资料,并可以逐步估计:t (cid:0) (cid:1) (xˆ) (xˆ) (xd (cid:15) (x) (x) (x:15) (x:15) (x:0:0 t) (x-) - 由于Eq. (4). (Stochastic reconstruction x p (x x) 也是有效的, 但我们不认为 0 → 0 t → 此处 , 因为它使扭曲更难评估 。) 图5显示了由此产生的CIFAR10测试集上的额定图.
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Original: At each time t, the distortion is calculated as the root mean (cid:112) squared error x xˆ 2/D, and the rate is calculated as the cumulative number of bits received 0 0 (cid:107) − (cid:107) so far at time t.
中文: 在每次t时,扭曲被计算为根平均(cid:112)平方误差××××2/D,而率被计算为截至时间t时得到的位数累计为0(cid:107)−(cid:107).
<a id="S0079"></a> Source: p.7 S0079
Original: The distortion decreases steeply in the low-rate region of the rate-distortion plot, indicating that the majority of the bits are indeed allocated to imperceptible distortions. 80 60 40 20 0 0 200 400 600 800 1,000 Reverse process steps (T − t) )ESMR(noitrotsiD 1.5 1 0.5 0 0 200 400 600 800 1,000 Reverse process steps (T − t) )mid/stib(etaR 80 60 40 20 0 0 0.5 1 1.5 Rate (bits/dim) )ESMR(noitrotsiD Figure 5: Unconditional CIFAR10 test set rate-distortion vs. time.
中文: 在速率扭曲地块的低速率区域,失真率急剧下降,表明大部分位数确实被分配到难以察觉的失真. 80 60 40 20 0 200 400 800 800 倒置工艺步骤(T-t) ESMR(NoitrotsiD 1.5 1 0.5 0 200 400 600 800 1000 倒置工艺步骤(T-t)) mid/tib(etaR 80 60 0 0 0 0.5 1 1.5 速率(bits/dim)) ESMR(noitrotsiD 图5:无条件的CIFAR10试验套速率-分流与时间.
<a id="S0080"></a> Source: p.7 S0080
Original: Distortion is measured in root mean squared error on a [0, 255] scale.
中文: 扭曲用根平均平方误差测量,一个[0,255]尺度.
<a id="S0081"></a> Source: p.7 S0081
Original: Progressive generation We also run a progressive unconditional generation process given by progressive decompression from random bits.
中文: 逐步生成 我们也在进行一个渐进的无条件生成过程, 由随机位的渐进解压。
<a id="S0082"></a> Source: p.7 S0082
Original: In other words, we predict the result of the reverse process, xˆ , while sampling from the reverse process using Algorithm 2.
中文: 换句话说,我们预测反向过程的结果xˆ,同时使用算法2从反向过程取样.
<a id="S0083"></a> Source: p.7 S0083
Original: Figures 6 and 10 show the 0 resulting sample quality of xˆ over the course of the reverse process.
中文: 图6和图10显示在倒转过程中XQQ的0样本质量。
<a id="S0084"></a> Source: p.7 S0084
Original: Large scale image features 0 appear first and details appear last.
中文: 大尺度图像特征 0 出现先,细节出现后.
<a id="S0085"></a> Source: p.7 S0085
Original: Figure 7 shows stochastic predictions x p (x x ) with x 0 θ 0 t t ∼ | frozen for various t.
中文: 图7显示xx p (x x) 的分解预测,其中x 0 θ 0 t | 为各种t被冻结.
<a id="S0086"></a> Source: p.7 S0086
Original: When t is small, all but fine details are preserved, and when t is large, only large scale features are preserved.
中文: T小的时候,除了细细的细节都保留了下来;而T大的时候,只保留了大尺度地貌.
<a id="S0087"></a> Source: p.7 S0087
Original: Perhaps these are hints of conceptual compression [18].
中文: 也许这些都是概念压缩的提示[18].
<a id="S0088"></a> Source: p.7 S0088
Original: Figure 6: Unconditional CIFAR10 progressive generation (xˆ over time, from left to right).
中文: 图6:无条件的CIFAR10 渐进生成(xˆ随着时间,从左到右).
<a id="S0089"></a> Source: p.7 S0089
Original: Extended samples 0 and sample quality metrics over time in the appendix (Figs. 10 and 14).
中文: 附录中的扩展样本0和样本质量衡量标准(图10和图14)。
<a id="S0090"></a> Source: p.7 S0090
Original: Figure 7: When conditioned on the same latent, CelebA-HQ 256 × 256 samples share high-level attributes.
中文: 图7:CelebA-HQ 256 × 256个样本在以同一潜伏性为条件时具有高水平属性。
<a id="S0091"></a> Source: p.7 S0091
Original: Bottom-right quadrants are x , and other quadrants are samples from p (x |x ). t θ 0 t Connection to autoregressive decoding Note that the variational bound (5) can be rewritten as: (cid:34) (cid:35) (cid:88) L = D (q(x ) p(x )) + E D (q(x x ) p (x x )) + H(x ) (16) KL T T q KL t 1 t θ t 1 t 0 (cid:107) − | (cid:107) − | t 1 ≥ (See Appendix A for a derivation.) Now consider setting the diffusion process length T to the dimensionality of the data, defining the forward process so that q(x x ) places all probability mass t 0 on x with the first t coordinates masked out (i.e. q(x x ) masks | out the tth coordinate), setting 0 t t 1 p(x ) to place all mass on a blank image, and, for th | e s−ake of argument, taking p (x x ) to T θ t 1 t − | 7
中文: 右下角四角体为x,而其他四角体为样本出自p (x ××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××(×××××××××××××××××××××××××××××××××××××××××××××××××××× 现在考虑将扩散过程的长度T设定为数据的可视性,定义前向过程,使q(xxx)将所有概率质量t0放入x上,并蒙住第一个t坐标(即q(xxx)口罩出tth坐标),设置0ttt 1 p(x)将所有质量放入空白图像上,对于QQ(e-s-ake)争论,取p(xx)t 1t-QQ 7
<a id="S0092"></a> Source: p.8 S0092
Original: Figure 8: Interpolations of CelebA-HQ 256x256 images with 500 timesteps of diffusion. be a fully expressive conditional distribution.
中文: 图8:CelebA-HQ 256x256图像被内入,传播时间为500分. 成为充分表达性有条件的分布.
<a id="S0093"></a> Source: p.8 S0093
Original: With these choices, D (q(x ) p(x )) = 0, and KL T T (cid:107) minimizing D (q(x x ) p (x x )) trains p to copy coordinates t + 1, . . . , T unchanged KL t 1 t θ t 1 t θ and to predict the tth co−ord | inat (cid:107) e given −t + | 1, . . . , T .
中文: 有了这些选择,D(q(x) p(x))=0,而KL T(cid:107)将D(q(xx) p(xx))列车p复制坐标t+1.,T不变的KLtt 1t 1t 并预言tth co-ord inat(cid:107) e给定-t + + 1,.,T.
<a id="S0094"></a> Source: p.8 S0094
Original: Thus, training p with this particular diffusion is θ training an autoregressive model.
中文: 因此,具有这种特别普及性的培训p是一种自发性模式的培训。
<a id="S0095"></a> Source: p.8 S0095
Original: We can therefore interpret the Gaussian diffusion model (2) as a kind of autoregressive model with a generalized bit ordering that cannot be expressed by reordering data coordinates.
中文: 因此,我们可以将高斯扩散模型(2)解释为一种自旋式模型,其通俗的位顺序不能通过重排数据坐标来表示.
<a id="S0096"></a> Source: p.8 S0096
Original: Prior work has shown that such reorderings introduce inductive biases that have an impact on sample quality [38], so we speculate that the Gaussian diffusion serves a similar purpose, perhaps to greater effect since Gaussian noise might be more natural to add to images compared to masking noise.
中文: 先前的研究表明,这种重排会引入对样本质量有影响的诱导偏差[38],因此我们推测高斯扩散具有类似的目的,也许效果更大,因为高斯噪音可能比遮掩噪音更自然地会增加图像.
<a id="S0097"></a> Source: p.8 S0097
Original: Moreover, the Gaussian diffusion length is not restricted to equal the data dimension; for instance, we use T = 1000, which is less than the dimension of the 32 32 3 or 256 256 3 images in our experiments. × × × × Gaussian diffusions can be made shorter for fast sampling or longer for model expressiveness. 4.4 Interpolation We can interpolate source images x , x q(x ) in latent space using q as a stochastic encoder, 0 (cid:48)0 ∼ 0 x , x q(x x ), then decoding the linearly interpolated latent x¯ = (1 λ)x + λx into image t (cid:48)t ∼ t | 0 t − 0 (cid:48)0 space by the reverse process, x¯ p(x x¯ ).
中文: 此外,高斯扩散长度并不局限于等于数据维度;例如,我们使用T=1000,这比我们实验中3232 3或256 256 3相片的维度还小. ××高斯散射可以作更短的快速采样,也可以作更长时间的模型表达. 4.4 内插 我们可以将源图像 x, x q (x) 在潜在空间中以 q 为分解编码器, 0 (cid:480 ∼, x q (x ×)), 然后通过反向过程将线性分解为 linear (1 λ)x + λ (cid:48t ∼ | (cid:48) → 0 (cid:48) 空间, x p (x ×).
<a id="S0098"></a> Source: p.8 S0098
Original: In effect, we use the reverse process to remove 0 0 t ∼ | artifacts from linearly interpolating corrupted versions of the source images, as depicted in Fig. 8 (left).
中文: 实际上,我们使用反向过程,从线性地插入已腐坏的源图像中去除0个t QQ的文物,如图8所描绘的.
<a id="S0099"></a> Source: p.8 S0099
Original: We fixed the noise for different values of λ so x and x remain the same.
中文: 我们固定了不同值的噪音,所以x和x保持不变。
<a id="S0100"></a> Source: p.8 S0100
Original: Fig. 8 (right) t (cid:48)t shows interpolations and reconstructions of original CelebA-HQ 256 256 images (t = 500).
中文: 图8 (右)t (cid:48t)显示原始 CelebA-HQ 256 256相片(t = 500相片)的插图与重建.
<a id="S0101"></a> Source: p.8 S0101
Original: The × reverse process produces high-quality reconstructions, and plausible interpolations that smoothly vary attributes such as pose, skin tone, hairstyle, expression and background, but not eyewear.
中文: ×倒置过程产生出高质量的重建,以及令人信服的插值,这些插值会平稳地改变各种属性,如姿势,皮肤色调,发型,表情和背景等,但不是眼衣.
<a id="S0102"></a> Source: p.8 S0102
Original: Larger t results in coarser and more varied interpolations, with novel samples at t = 1000 (Appendix Fig. 9). 5 Related Work While diffusion models might resemble flows [9, 46, 10, 32, 5, 16, 23] and VAEs [33, 47, 37], diffusion models are designed so that q has no parameters and the top-level latent x has nearly zero T mutual information with the data x .
中文: 较大的t得到更相近和更相异的插值,出自t=1000的小说样本(附录图9). 5 相关工作 虽然扩散模型可能类似于流 [9, 46, 10, 32, 5, 16, 23] 和 VAEs [33, 47, 37],但扩散模型的设计使得q没有参数,而顶层潜入x与数据x的相互信息几乎为零.
<a id="S0103"></a> Source: p.8 S0103
Original: Our (cid:15)-prediction reverse process parameterization establishes a 0 connection between diffusion models and denoising score matching over multiple noise levels with annealed Langevin dynamics for sampling [55, 56].
中文: 我们的(cid:15)-预测反向过程参数化在扩散模型和去诺比分在多噪量水平上与被厌杀的朗格文动力学相匹配以进行取样[55,56]之间建立了0连接.
<a id="S0104"></a> Source: p.8 S0104
Original: Diffusion models, however, admit straightforward log likelihood evaluation, and the training procedure explicitly trains the Langevin dynamics sampler using variational inference (see Appendix C for details).
中文: 然而,传播模型承认了直截了当的日志概率评估,培训程序通过可变推论(详见附录C)明确培训了Langevin动态取样器.
<a id="S0105"></a> Source: p.8 S0105
Original: The connection also has the reverse implication that a certain weighted form of denoising score matching is the same as variational inference to train a Langevin-like sampler.
中文: 连接还具有相反的含义,即某种加权形式的去诺比分比对等于可变推论来训练类似朗格文的采样器.
<a id="S0106"></a> Source: p.8 S0106
Original: Other methods for learning transition operators of Markov chains include infusion training [2], variational walkback [15], generative stochastic networks [1], and others [50, 54, 36, 42, 35, 65].
中文: 学习马尔可夫链的过渡操作员的其他方法有:倒注训练[2],可变回行走[15],基因分层网络[1],而其他[50,54,36,42,35,65].
<a id="S0107"></a> Source: p.8 S0107
Original: By the known connection between score matching and energy-based modeling, our work could have implications for other recent work on energy-based models [67–69, 12, 70, 13, 11, 41, 17, 8].
中文: 通过分数比对和以能为基础的模型的已知联系,我们的工作可能对最近关于以能为基础的模型的其他工作[67-69,12,70,13,11,41,17,8]产生影响.
<a id="S0108"></a> Source: p.8 S0108
Original: Our rate-distortion curves are computed over time in one evaluation of the variational bound, reminiscent of how rate-distortion curves can be computed over distortion penalties in one run of annealed importance sampling [24].
中文: 我们的速率扭曲曲线是随着时间的推移在一次对变异约束的评价中计算出来的,这让人想起了在一次无源重要采样[24]中,速率扭曲曲线的计算方法可以超过被扭曲的处罚。
<a id="S0109"></a> Source: p.8 S0109
Original: Our progressive decoding argument can be seen in convolutional DRAW and related models [18, 40] and may also lead to more general designs for subscale orderings or sampling strategies for autoregressive models [38, 64]. 8
中文: 我们的渐进解码论点可以从革命性DRAW和相关模型[18,40]中看出,并且还可能导致更一般地设计出自旋模型的分尺度订购或采样策略[38,64]. 8
<a id="S0110"></a> Source: p.9 S0110
Original: 6 Conclusion We have presented high quality image samples using diffusion models, and we have found connections among diffusion models and variational inference for training Markov chains, denoising score matching and annealed Langevin dynamics (and energy-based models by extension), autoregressive models, and progressive lossy compression.
中文: 6 结论 我们利用扩散模型提出了高质量的图像样本,我们发现扩散模型和变异推论之间的联系,用于培训马尔可夫链条,去诺比分和厌去Langevin动力学(以及扩展的以能为基础的模型),自相递进模型,以及渐进的损耗压缩.
<a id="S0111"></a> Source: p.9 S0111
Original: Since diffusion models seem to have excellent inductive biases for image data, we look forward to investigating their utility in other data modalities and as components in other types of generative models and machine learning systems.
中文: 由于扩散模型似乎对图像数据有极好的诱导偏差,我们期待着调查这些模型在其他数据模式中的效用,以及作为其他类型基因模型和机器学习系统的组成部分。
<a id="S0112"></a> Source: p.9 S0112
Original: Broader Impact Our work on diffusion models takes on a similar scope as existing work on other types of deep generative models, such as efforts to improve the sample quality of GANs, flows, autoregressive models, and so forth.
中文: 更大的影响 我们有关扩散模型的工作,其范围与其他类型的深层遗传模型的现有工作相类似,例如努力提高GAN的样本质量,流量,自转模型等.
<a id="S0113"></a> Source: p.9 S0113
Original: Our paper represents progress in making diffusion models a generally useful tool in this family of techniques, so it may serve to amplify any impacts that generative models have had (and will have) on the broader world.
中文: 我们的文件表明,在使传播模型成为这一技术体系中普遍有用的工具方面取得了进展,因此,它可能有助于扩大遗传模型已经(和将要)对更广大世界的任何影响。
<a id="S0114"></a> Source: p.9 S0114
Original: Unfortunately, there are numerous well-known malicious uses of generative models.
中文: 不幸的是,对基因模型有许多众所周知的恶意用途。
<a id="S0115"></a> Source: p.9 S0115
Original: Sample generation techniques can be employed to produce fake images and videos of high profile figures for political purposes.
中文: 可以采用样本生成技术,为政治目的制作高知名度人物的假相和视频.
<a id="S0116"></a> Source: p.9 S0116
Original: While fake images were manually created long before software tools were available, generative models such as ours make the process easier.
中文: 虽然假图像是在软件工具提供之前很久才手工创建的,但像我们这样的基因模型使得这一过程变得更容易.
<a id="S0117"></a> Source: p.9 S0117
Original: Fortunately, CNN-generated images currently have subtle flaws that allow detection [62], but improvements in generative models may make this more difficult.
中文: 幸运的是,CNN生成的图像目前有微妙的缺陷,可以被检测出[62],但基因模型的改进可能使这一困难更大.
<a id="S0118"></a> Source: p.9 S0118
Original: Generative models also reflect the biases in the datasets on which they are trained.
中文: 遗传模型还反映了培训对象数据集的偏差。
<a id="S0119"></a> Source: p.9 S0119
Original: As many large datasets are collected from the internet by automated systems, it can be difficult to remove these biases, especially when the images are unlabeled.
中文: 由于许多大型数据集是通过自动化系统从互联网上收集的,因此可能很难去除这些偏差,特别是在图像没有标签的情况下.
<a id="S0120"></a> Source: p.9 S0120
Original: If samples from generative models trained on these datasets proliferate throughout the internet, then these biases will only be reinforced further.
中文: 如果通过这些数据集培训的基因模型样本在互联网上扩散,那么这些偏见只会得到进一步的强化。
<a id="S0121"></a> Source: p.9 S0121
Original: On the other hand, diffusion models may be useful for data compression, which, as data becomes higher resolution and as global internet traffic increases, might be crucial to ensure accessibility of the internet to wide audiences.
中文: 另一方面,传播模型可能对数据压缩有用,随着数据分辨率的提高和全球互联网流量的增加,数据压缩对于确保广大受众能够使用互联网可能至关重要。
<a id="S0122"></a> Source: p.9 S0122
Original: Our work might contribute to representation learning on unlabeled raw data for a large range of downstream tasks, from image classification to reinforcement learning, and diffusion models might also become viable for creative uses in art, photography, and music.
中文: 我们的工作可能有助于从图像分类到强化学习等一系列下游任务的无标签原始数据方面的代表性学习,传播模式也可能成为艺术、摄影和音乐的创造性用途。
<a id="S0123"></a> Source: p.9 S0123
Original: Acknowledgments and Disclosure of Funding This work was supported by ONR PECASE and the NSF Graduate Research Fellowship under grant number DGE-1752814.
中文: 资金的确认和披露 这项工作得到了挪威国家科学研究署和NSF研究生研究研究金的支持,赠款编号为DGE-1752814。
<a id="S0124"></a> Source: p.9 S0124
Original: Google’s TensorFlow Research Cloud (TFRC) provided Cloud TPUs.
中文: Google的TensorFlow研究云(TFRC)提供了Cloud TPU.
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中文: 你的分类器是一个基于能量的模型 你应该把它当成一个模型
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中文: 关联性的沟通复杂性.
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Original: Evaluating lossy compression rates of deep generative models.
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Original: Markov Chain Monte Carlo and variational inference: Bridging the gap.
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Original: PixelCNN++: Improving the PixelCNN with discretized logistic mixture likelihood and other modifications.
中文: 像素CNN++: 改进PixelCNN,使其具有磁盘化后勤混合物的可能性并作其他修改。
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Original: Deep unsupervised learning using nonequilibrium thermodynamics.
中文: 利用无平衡热力学进行深度无监督学习.
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Original: Generative modeling by estimating gradients of the data distribution.
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Original: Conditional image generation with PixelCNN decoders.
中文: 用 PixelCNN 解码器生成有条件的图像 。
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Original: Cnn-generated images are surprisingly easy to spot...for now.
中文: 现在Cnn生成的图像很容易发现
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Original: Predictive sampling with forecasting autoregressive models. arXiv preprint arXiv:2002.09928, 2020. [65] Hao Wu, Jonas Köhler, and Frank Noé.
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Original: Synthesizing dynamic patterns by spatial-temporal generative convnet.
中文: 由空间-时相基因整流网合成动态模式.
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Original: Learning descriptor networks for 3d shape synthesis and analysis.
中文: 学习描述网络用于3d形状合成和分析.
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Original: Learning energy-based spatial-temporal generative convnets for dynamic patterns.
中文: 学习以能为基础的空间-时序基因圈来适应动态规律.
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Original: LSUN: Construction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015. [72] Sergey Zagoruyko and Nikos Komodakis.
中文: LSUN:利用环中与人类的深度学习来构建大型图像数据集. arXiv preprint arXiv:1506.03365, 2015. [72] 谢尔盖·扎戈鲁伊科和尼科斯·克莫达基斯.
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Original: Wide residual networks. arXiv preprint arXiv:1605.07146, 2016. 12
中文: 广余网. arXiv预印 arXiv:1605.07146, 2016. 12 (英语).
<a id="S0245"></a> Source: p.13 S0245
Original: Extra information LSUN FID scores for LSUN datasets are included in Table 3.
中文: LSUN数据集的额外信息LSUN FID分数见表3.
<a id="S0246"></a> Source: p.13 S0246
Original: Scores marked with are reported ∗ by StyleGAN2 as baselines, and other scores are reported by their respective authors.
中文: 标有*的分数由StyleGAN2报告为基线,其他分数由各自的作者报告.
<a id="S0247"></a> Source: p.13 S0247
Original: Table 3: FID scores for LSUN 256 256 datasets × Model LSUN Bedroom LSUN Church LSUN Cat ProgressiveGAN [27] 8.34 6.42 37.52 StyleGAN [28] 2.65 4.21 8.53 ∗ ∗ StyleGAN2 [30] - 3.86 6.93 Ours (L ) 6.36 7.89 19.75 simple Ours (L , large) 4.90 - simple Progressive compression Our lossy compression argument in Section 4.3 is only a proof of concept, because Algorithms 3 and 4 depend on a procedure such as minimal random coding [20], which is not tractable for high dimensional data.
中文: 表3: LSUN 256 256个数据集的FID分数 × Model LSUN Bedroom LSUN Church LSUN Cat ProgressGAN [27] 8.34 6.42 37.52 StyleGAN [28] 2.65 4.21 8.53 StyleGAN2 [30] - 3.86 6.93 Ours (L) 6.36 7.89 19.75 简单 Ours (L,大) 4.90 - 简单进取压缩 我们在"4.3节"中的损失压缩论证只是概念的证明,因为算法3和4依赖于最小随机编码等程序[20],对于高维度数据是无法被取取取的.
<a id="S0248"></a> Source: p.13 S0248
Original: These algorithms serve as a compression interpretation of the variational bound (5) of Sohl-Dickstein et al. [53], not yet as a practical compression system.
中文: 这些算法充当了Sohl-Dickstein等[53]的变异约束(5)的压缩解释,还不是实用的压缩系统.
<a id="S0249"></a> Source: p.13 S0249
Original: Table 4: Unconditional CIFAR10 test set rate-distortion values (accompanies Fig. 5) Reverse process time (T t + 1) Rate (bits/dim) Distortion (RMSE [0, 255]) − 1000 1.77581 0.95136 900 0.11994 12.02277 800 0.05415 18.47482 700 0.02866 24.43656 600 0.01507 30.80948 500 0.00716 38.03236 400 0.00282 46.12765 300 0.00081 54.18826 200 0.00013 60.97170 100 0.00000 67.60125 A Extended derivations Below is a derivation of Eq. (5), the reduced variance variational bound for diffusion models.
中文: 表4:无条件的CIFAR10试验集速率扭曲值(并附图5) 逆向过程时间(T t + 1) 速率(位/分) 扭曲(RMSE [0, 255]) − 1000 1.77581 0.95136 900 12.02277 800 0.05415 18.47482 700 0.0282 700 0.0286 24.43656 600 0.01507 30.80948 500 0.00716 38.03236 400 0.0282 46.12765 300 0.00081 54.18826 200 0.0001360170 100 0.00067.60125 扩展衍生物是Eq (5)的衍生物,其变异性减少,受扩散模型约束。
<a id="S0250"></a> Source: p.13 S0250
Original: This material is from Sohl-Dickstein et al. [53]; we include it here only for completeness. (cid:20) (cid:21) p (x ) L = E log θ 0:T (17) q − q(x x ) 1:T 0 | = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) (18) − − q(x x ) t t 1 t 1 | − ≥ (cid:34) (cid:35) = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) log p θ (x 0 | x 1 ) (19) − − q(x x ) − q(x x ) t t 1 1 0 t>1 | − | (cid:34) (cid:35) = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) q(x t − 1 | x 0 ) log p θ (x 0 | x 1 ) (20) − − q(x x , x ) · q(x x ) − q(x x ) t 1 t 0 t 0 1 0 t>1 − | | | (cid:34) (cid:35) = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) log p θ (x 0 x 1 ) (21) − q(x x ) − q(x x , x ) − | T 0 t 1 t 0 | t>1 − | 13
中文: 这些材料取自Sohl-Dickstein等人[53];我们只为了完整性而将其列入此处. (cid:20) (cid:21) p (x:20) L = Elog → 0:T (17) q (x:34) (cid:35) = Eq → q (x:18) = (x:88) = (x:1) − (x:18) q (x:13) t (x:34) (x:35) → Eq → (17) q (x:17) q (x:18) q (x:17) q (x:17) q (x:17) q (x:18) q (x:18-18) | (x-18-18) q (x-18) | (x-18) | (x-18-18) | (x) | (x-18-18) | (x-18-18-18) | (x-18-18) | (x-18-18-) | (x-18-) | (x-18-) | (x-18-
<a id="S0251"></a> Source: p.14 S0251
Original: (cid:34) (cid:35) (cid:88) = E D (q(x x ) p(x )) + D (q(x x , x ) p (x x )) log p (x x ) q KL T 0 T KL t 1 t 0 θ t 1 t θ 0 1 | (cid:107) − | (cid:107) − | − | t>1 (22) The following is an alternate version of L.
中文: (编:34) (编:35) (编:88) = E D (q (xx) p (xx)) + D (q (xxx) p (xxx)) log p (xxx) q KL T 0 T KL t 1 t 1 t 1 t → (编:107) → (cid:107) → (xxx) 1 (22) 以下为L.
<a id="S0252"></a> Source: p.14 S0252
Original: It is not tractable to estimate, but it is useful for our discussion in Section 4.3. L = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) (23) − − q(x x ) t t 1 t 1 | − ≥ = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) q(x t − 1 ) (24) − − q(x x ) · q(x ) t 1 t t t 1 − | ≥ = E q log p(x T ) (cid:88) log p θ (x t − 1 | x t ) log q(x 0 ) (25) − q(x ) − q(x x ) − T t 1 t t 1 − | ≥ (cid:88) = D KL (q(x T ) p(x T )) + E q D KL (q(x t 1 x t ) p θ (x t 1 x t )) + H(x 0 ) (26) (cid:107) − | (cid:107) − | t 1 ≥ B Experimental details Our neural network architecture follows the backbone of PixelCNN++ [52], which is a U-Net [48] based on a Wide ResNet [72].
中文: 无法估计,但对于我们在4.3节中的讨论有用。 L = E q log p (x T) (cid:88) log p (x t- 1 | x x (23)- q (x x ≥ q q q) (cid:88) log p (x |) (x t | | | | | | | q q q q q (x 25) 25) 25) 88) ) )) (x 25) 25) 25) q q 25) q q q q q q q q q q q q q q q q q q q q q | q q | q | | q | | | q q q q q q q q q q q q q q q q q q q q q q
<a id="S0253"></a> Source: p.14 S0253
Original: We replaced weight normalization [49] with group normalization [66] to make the implementation simpler.
中文: 我们把重量正常化[49]取而代之的是集团正常化[66],以简化执行工作。
<a id="S0254"></a> Source: p.14 S0254
Original: Our 32 32 models use four feature map resolutions (32 32 × × to 4 4), and our 256 256 models use six.
中文: 我们的32个模型使用4个地物图分辨率(32 32 ××××到4 4),我们的256 256个模型使用6个.
<a id="S0255"></a> Source: p.14 S0255
Original: All models have two convolutional residual blocks × × per resolution level and self-attention blocks at the 16 16 resolution between the convolutional × blocks [6].
中文: 所有型号均有两块相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相接相
<a id="S0256"></a> Source: p.14 S0256
Original: Diffusion time t is specified by adding the Transformer sinusoidal position embedding [60] into each residual block.
中文: 分化时间t通过将变形器sinusoidal位置嵌入到每个剩余块来指定. [60].
<a id="S0257"></a> Source: p.14 S0257
Original: Our CIFAR10 model has 35.7 million parameters, and our LSUN and CelebA-HQ models have 114 million parameters.
中文: 我们的CIFAR10模型有3570万个参数,我们的LSUN和CelebA-HQ模型有1.14亿个参数.
<a id="S0258"></a> Source: p.14 S0258
Original: We also trained a larger variant of the LSUN Bedroom model with approximately 256 million parameters by increasing filter count.
中文: 我们还通过增加滤波计数,培训了LSUN卧室模型的较大变体,参数约为2.56亿个.
<a id="S0259"></a> Source: p.14 S0259
Original: We used TPU v3-8 (similar to 8 V100 GPUs) for all experiments.
中文: 我们在所有实验中使用了TPU v3-8(类似于8个V100 GPU).
<a id="S0260"></a> Source: p.14 S0260
Original: Our CIFAR model trains at 21 steps per second at batch size 128 (10.6 hours to train to completion at 800k steps), and sampling a batch of 256 images takes 17 seconds.
中文: 我国CIFAR型号列车以每秒21步128分(10.6小时以800克步来进行训练以完成),并抽取了一批256幅图像需要17秒.
<a id="S0261"></a> Source: p.14 S0261
Original: Our CelebA-HQ/LSUN (2562) models train at 2.2 steps per second at batch size 64, and sampling a batch of 128 images takes 300 seconds.
中文: 我们的CelebA-HQ/LSUN (2562)型号列车在批量尺寸为64时每秒2.2步,并抽取了一批128个图像需要300秒.
<a id="S0262"></a> Source: p.14 S0262
Original: We trained on CelebA-HQ for 0.5M steps, LSUN Bedroom for 2.4M steps, LSUN Cat for 1.8M steps, and LSUN Church for 1.2M steps.
中文: 我们在CelebA-HQ训练了0.5M步,LSUN卧室训练了2.4M步,LSUN Cat训练了1.8M步,LSUN Church训练了1.2M步.
<a id="S0263"></a> Source: p.14 S0263
Original: The larger LSUN Bedroom model was trained for 1.15M steps.
中文: 更大的LSUN卧室模型接受了1.15M阶梯的训练.
<a id="S0264"></a> Source: p.14 S0264
Original: Apart from an initial choice of hyperparameters early on to make network size fit within memory constraints, we performed the majority of our hyperparameter search to optimize for CIFAR10 sample quality, then transferred the resulting settings over to the other datasets: • We chose the β schedule from a set of constant, linear, and quadratic schedules, all t constrained so that L 0.
中文: 除了早期初步选择超参数使网络大小适应内存限制外,我们进行了大多数超参数搜索,以优化CIFAR10样本质量,然后将由此产生的设置转移到其他数据集: • 我们从一组恒定的,线性的,和四面体的时间表中选择了β表, 全部被限制到L 0。
<a id="S0265"></a> Source: p.14 S0265
Original: We set T = 1000 without a sweep, and we chose a linear T schedule from β = 10 ≈4 to β = 0.02. 1 − T • We set the dropout rate on CIFAR10 to 0.1 by sweeping over the values 0.1, 0.2, 0.3, 0.4 . { } Without dropout on CIFAR10, we obtained poorer samples reminiscent of the overfitting artifacts in an unregularized PixelCNN++ [52].
中文: 我们设定 T = 1000 没有扫描,我们选择了从 β = 10 X 4 到 β = 0.02的线性 T 时间表. 1-T − 我们通过扫码0.1、0.2、0.3、0.4,将CIFAR10的辍学率确定为0.1。 在CIFAR10没有辍学的情况下,我们获得了较贫穷的样本,让人联想出一种未规范的PixelCNN++ [52].
<a id="S0266"></a> Source: p.14 S0266
Original: We set dropout rate on the other datasets to zero without sweeping. • We used random horizontal flips during training for CIFAR10; we tried training both with and without flips, and found flips to improve sample quality slightly.
中文: 我们把其他数据集的辍学率确定为零而不扫地。 我们在训练CIFAR10时使用了随机水平翻转;我们尝试了无论有无翻转的训练,并发现了翻转来略微提高样本质量.
<a id="S0267"></a> Source: p.14 S0267
Original: We also used random horizontal flips for all other datasets except LSUN Bedroom. • We tried Adam [31] and RMSProp early on in our experimentation process and chose the former.
中文: 除了LSUN Bedroom之外,我们还对所有其他数据集使用随机水平翻转。
<a id="S0268"></a> Source: p.14 S0268
Original: We left the hyperparameters to their standard values.
中文: 我们把超参数留给他们的标准值
<a id="S0269"></a> Source: p.14 S0269
Original: We set the learning rate to 2 10 4 without any sweeping, and we lowered it to 2 10 5 for the 256 256 images, − − × × × which seemed unstable to train with the larger learning rate. 14
中文: 我们把256个256个图像的学习率设定为2 10 4, 并且我们把它降为2 10 5, —— —— —— —— —— —— —— 这似乎不稳定, 无法用更大的学习率来训练。 页:1
<a id="S0270"></a> Source: p.15 S0270
Original: • We set the batch size to 128 for CIFAR10 and 64 for larger images.
中文: • 我们规定CIFAR10的批量尺寸为128个,大图像为64个。
<a id="S0271"></a> Source: p.15 S0271
Original: We did not sweep over these values. • We used EMA on model parameters with a decay factor of 0.9999.
中文: 我们没有扫荡这些价值观。 我们在模型参数上使用了EMA,衰变系数为0.9999.
<a id="S0272"></a> Source: p.15 S0272
Original: Final experiments were trained once and evaluated throughout training for sample quality.
中文: 最后的实验经过一次培训,并在整个培训中评价样品质量。
<a id="S0273"></a> Source: p.15 S0273
Original: Sample quality scores and log likelihood are reported on the minimum FID value over the course of training.
中文: 在培训过程中,报告质量样本分数和记录可能性,说明最低FID值。
<a id="S0274"></a> Source: p.15 S0274
Original: On CIFAR10, we calculated Inception and FID scores on 50000 samples using the original code from the OpenAI [51] and TTUR [21] repositories, respectively.
中文: 在CIFAR10上,我们分别使用OpenAI [51]和TTUR [21]寄存器的原始代码,计算出5000个样本的受测分和FID分.
<a id="S0275"></a> Source: p.15 S0275
Original: On LSUN, we calculated FID scores on 50000 samples using code from the StyleGAN2 [30] repository.
中文: 在LSUN上,我们用StyleGAN2[30]寄存器的代码计算出50000个样本的FID分数.
<a id="S0276"></a> Source: p.15 S0276
Original: CIFAR10 and CelebA-HQ were loaded as provided by TensorFlow Datasets (https://www.tensorflow.org/datasets), and LSUN was prepared using code from StyleGAN.
中文: CIFAR10和CelebA-HQ由TensorFlow Datasets(https://www.tensorflow.org/datasets)提供上载,LSUN是使用StyleGAN的代码编写的.
<a id="S0277"></a> Source: p.15 S0277
Original: Dataset splits (or lack thereof) are standard from the papers that introduced their usage in a generative modeling context.
中文: 数据集分拆(或缺乏分拆)是那些在基因模型上下文中引入其用法的论文的标准.
<a id="S0278"></a> Source: p.15 S0278
Original: All details can be found in the source code release. C Discussion on related work Our model architecture, forward process definition, and prior differ from NCSN [55, 56] in subtle but important ways that improve sample quality, and, notably, we directly train our sampler as a latent variable model rather than adding it after training post-hoc.
中文: 所有细节均可在源代码发布中找到. C 相关工作的讨论 我们的模型架构,前向过程定义,以及先前与NCSN[55,56]在提高样本质量的微妙而重要的方式上有所不同,特别是,我们直接培训我们的样本员,将其作为潜在的可变模型,而不是在培训后添加.
<a id="S0279"></a> Source: p.15 S0279
Original: We use a U-Net with self-attention; NCSN uses a RefineNet with dilated convolutions.
中文: 我们使用一个自觉的U-Net;NCSN使用一个有膨胀分解分解的FineNet.
<a id="S0280"></a> Source: p.15 S0280
Original: We condition all layers on t by adding in the Transformer sinusoidal position embedding, rather than only in normalization layers (NCSNv1) or only at the output (v2). 2.
中文: 我们通过在变形器 sinosoidal 位置上添加嵌入来附加所有层在t上,而不只是在正态层(NCSNv1)上,或者只在输出(v2)上. 2. 联合国
<a id="S0281"></a> Source: p.15 S0281
Original: Diffusion models scale down the data with each forward process step (by a √1 β factor) t − so that variance does not grow when adding noise, thus providing consistently scaled inputs to the neural net reverse process.
中文: 分流模型用每个前向过程步骤(用"% 1 β 系数"来缩放数据 t-,这样在增加噪声时差异不会增大,从而为神经网倒转过程提供一致的分量输入.
<a id="S0282"></a> Source: p.15 S0282
Original: Unlike NCSN, our forward process destroys signal (D (q(x x ) (0, I)) 0), ensur- KL T 0 | (cid:107) N ≈ ing a close match between the prior and aggregate posterior of x .
中文: 与NSCN不同的是,我们的前进过程会破坏信号(D (q (x x (0, I)))0),随后的- KL T 0 → (cid:107) N → 将前后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后后
<a id="S0283"></a> Source: p.15 S0283
Original: Also unlike NCSN, our T β are very small, which ensures that the forward process is reversible by a Markov chain t with conditional Gaussians.
中文: 与NSCN不同的是,我们的Tβ非常小,这保证了前向过程被有条件的高斯人所组成的马尔可夫链t所可逆.
<a id="S0284"></a> Source: p.15 S0284
Original: Both of these factors prevent distribution shift when sampling. 4.
中文: 这两个因素都防止了取样时的分布转移. 4.四.
<a id="S0285"></a> Source: p.15 S0285
Original: Our Langevin-like sampler has coefficients (learning rate, noise scale, etc.) derived rigorously from β in the forward process.
中文: 我们的Langevin类采样器的系数(学习率、噪音尺度等)严格来自远期过程中的β。
<a id="S0286"></a> Source: p.15 S0286
Original: Thus, our training procedure directly trains our t sampler to match the data distribution after T steps: it trains the sampler as a latent variable model using variational inference.
中文: 因此,我们的培训程序直接培训我们的 t 采样器,以匹配T步骤后的数据分布:它利用可变推论,将采样器培训为潜在的可变模型.
<a id="S0287"></a> Source: p.15 S0287
Original: In contrast, NCSN’s sampler coefficients are set by hand post-hoc, and their training procedure is not guaranteed to directly optimize a quality metric of their sampler. D Samples Additional samples Figure 11, 13, 16, 17, 18, and 19 show uncurated samples from the diffusion models trained on CelebA-HQ, CIFAR10 and LSUN datasets.
中文: 相形之下,NCSN的采样器系数是用手定出后荷克的,他们的训练程序不能保证直接优化其取样器的质量度量. D. 补充样品 图11、13、16、17、18和19显示关于CelebA-HQ、CIFAR10和LSUN数据集培训的传播模型的未检验样品。
<a id="S0288"></a> Source: p.15 S0288
Original: Latent structure and reverse process stochasticity During sampling, both the prior x T ∼ (0, I) and Langevin dynamics are stochastic.
中文: 在采样过程中,先期X T (0, I) 和朗格文动力学都是有花样的。
<a id="S0289"></a> Source: p.15 S0289
Original: To understand the significance of the second source N of noise, we sampled multiple images conditioned on the same intermediate latent for the CelebA 256 256 dataset.
中文: 为了了解噪音的第二源N的意义,我们取样了以同一中间潜伏物为条件的多种图像,用于CelebA 256 256数据集.
<a id="S0290"></a> Source: p.15 S0290
Original: Figure 7 shows multiple draws from the reverse process x p (x x ) that 0 θ 0 t × ∼ | share the latent x for t 1000, 750, 500, 250 .
中文: 图7显示,从逆向过程取自的乘数xp (xx)为0 θ 0 t | | | 为t 1000, 750, 500, 250 分享了潜入的乘数x.
<a id="S0291"></a> Source: p.15 S0291
Original: To accomplish this, we run a single reverse chain t ∈ { } from an initial draw from the prior.
中文: 为了完成这个任务,我们从前作的初始抽取中运行一个单反向链 t {{}.
<a id="S0292"></a> Source: p.15 S0292
Original: At the intermediate timesteps, the chain is split to sample multiple images.
中文: 在中间时序,链被分出来取取多个图像样本.
<a id="S0293"></a> Source: p.15 S0293
Original: When the chain is split after the prior draw at x , the samples differ significantly. T =1000 However, when the chain is split after more steps, samples share high-level attributes like gender, hair color, eyewear, saturation, pose and facial expression.
中文: 当链在上图后以 x 进行分解时,样品差异很大. 页:1 然而,当链被分出更多的步骤后,样品会分享性别,发色,眼衣,饱和,姿势和面部表情等高层次属性.
<a id="S0294"></a> Source: p.15 S0294
Original: This indicates that intermediate latents like x encode these attributes, despite their imperceptibility. 750 Coarse-to-fine interpolation Figure 9 shows interpolations between a pair of source CelebA 256 256 images as we vary the number of diffusion steps prior to latent space interpolation. × Increasing the number of diffusion steps destroys more structure in the source images, which the 15
中文: 这表明,像x这样的中间潜伏物编码了这些属性,尽管其不可接受. 750 从粗到细的内插图图图9显示了一对源CelebA 256 256个图像之间的内插图,因为我们在潜在空间内插前会改变扩散步骤的数量. × 增加扩散步骤的数量会破坏源图像中更多的结构,15
<a id="S0295"></a> Source: p.16 S0295
Original: model completes during the reverse process.
中文: 模型在倒转过程中完成.
<a id="S0296"></a> Source: p.16 S0296
Original: This allows us to interpolate at both fine granularities and coarse granularities.
中文: 这使得我们可以在细颗粒物和粗颗粒物上进行插接.
<a id="S0297"></a> Source: p.16 S0297
Original: In the limiting case of 0 diffusion steps, the interpolation mixes source images in pixel space.
中文: 在0扩散步骤的限制下,插值将源图像混合到像素空间.
<a id="S0298"></a> Source: p.16 S0298
Original: On the other hand, after 1000 diffusion steps, source information is lost and interpolations are novel samples.
中文: 另一方面,在1000个扩散步骤后,源信息丢失了,插图是新颖的样本.
<a id="S0299"></a> Source: p.16 S0299
Original: Source Rec. λ=0.1 λ=0.2 λ=0.3 λ=0.4 λ=0.5 λ=0.6 λ=0.7 λ=0.8 λ=0.9 Rec.
中文: 来源 注释 0.1 λ= 0.2 λ= 0.3 λ= 0.4 λ= 0.5 λ= 0.6 λ= 0.7 λ= 0.8 λ= 0.9 Rec Rec Rec Rec Rec Rec Rec Rec
<a id="S0300"></a> Source: p.16 S0300
Original: Source 1000 steps 875 steps 750 steps 625 steps 500 steps 375 steps 250 steps 125 steps 0 steps Figure 9: Coarse-to-fine interpolations that vary the number of diffusion steps prior to latent mixing. 10 8 6 4 2 0 200 400 600 800 1,000 Reverse process steps (T − t) erocSnoitpecnI 300 200 100 0 0 200 400 600 800 1,000 Reverse process steps (T − t) DIF Figure 10: Unconditional CIFAR10 progressive sampling quality over time 16
中文: 出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出自出 10 8 6 4 2 0 200 400 600 800 000 倒置工艺步骤(T - t) erocSnoitpecnI 300 200 100 0 200 400 600 800 000 图10:无条件的CIFAR10 逐步取样质量
<a id="S0301"></a> Source: p.17 S0301
Original: Figure 11: CelebA-HQ 256 256 generated samples × 17
中文: 图11:CelebA-HQ 256 256个生成的样本x17
<a id="S0302"></a> Source: p.18 S0302
Original: (a) Pixel space nearest neighbors (b) Inception feature space nearest neighbors Figure 12: CelebA-HQ 256 256 nearest neighbors, computed on a 100 100 crop surrounding the × × faces.
中文: (a) 相距最近的像素空间 (b) 相距最近的空间(Inception)
<a id="S0303"></a> Source: p.18 S0303
Original: Generated samples are in the leftmost column, and training set nearest neighbors are in the remaining columns. 18
中文: 生成的样本在最左边的一列,而培训的一列最近的邻居在其余一列. 第 18 条
<a id="S0304"></a> Source: p.19 S0304
Original: Figure 13: Unconditional CIFAR10 generated samples 19
中文: 图13:无条件生成的CIFAR10样本 19
<a id="S0305"></a> Source: p.20 S0305
Original: Figure 14: Unconditional CIFAR10 progressive generation 20
中文: 图14:无条件的CIFAR10逐步生成 20
<a id="S0306"></a> Source: p.21 S0306
Original: (a) Pixel space nearest neighbors (b) Inception feature space nearest neighbors Figure 15: Unconditional CIFAR10 nearest neighbors.
中文: (a) 距离最近的像素空间 (b) Inception 特征为距离最近的空间 图15:无条件的CIFAR10 距离最近的邻居。
<a id="S0307"></a> Source: p.21 S0307
Original: Generated samples are in the leftmost column, and training set nearest neighbors are in the remaining columns. 21
中文: 生成的样本在最左边的一列,而培训的一列最近的邻居在其余一列. 21国
<a id="S0308"></a> Source: p.22 S0308
Original: Figure 16: LSUN Church generated samples.
中文: 图16: LSUN Church生成了样本.
<a id="S0309"></a> Source: p.23 S0309
Original: Figure 17: LSUN Bedroom generated samples, large model.
中文: 图17: LSUN 卧室生成样品,大型模型.
<a id="S0310"></a> Source: p.24 S0310
Original: Figure 18: LSUN Bedroom generated samples, small model.
中文: 图18: LSUN 卧室生成样品,小型模型.