Paper Verified · TPAMI 2023

Diffusion Models
in Vision

一份面向推导、实现与证据边界的深度精读：把 DDPM、NCSN 与连续时间 SDE 放进同一坐标系，重建综述收录的全部方法分类，并解释这篇 2023 年历史综述能够证明什么。

Croitoru 与 Hondru 共同第一作者IEEE TPAMI 45(9): 10850–10869DOI 10.1109/TPAMI.2023.3261988阅读底稿 arXiv v5 · 2023-04-01最新 arXiv v6 · 2025-01-16

论文身份与版本边界

本页完整精读本地归档的 25 页 arXiv v5。arXiv 当前版本为 v6；逐行比较 v5 与 v6 的 25 页文本和 TeX 后，变化集中在排版、符号间距及少量语句修订，分类表和讨论范围没有扩充到 2025 年方法。

正式书目

IEEE TPAMI

2023 年第 45 卷第 9 期，10850–10869 页。正式标题是 Diffusion Models in Vision: A Survey。

作者角色

共同第一与通讯

PDF 脚注明确 Florinel-Alin Croitoru 与 Vlad Hondru 贡献相同；Radu Tudor Ionescu 由星号及邮箱明确标记为通讯作者。

材料范围

历史快照

综述主体覆盖到 2022 年左右的工作。Stable Diffusion 等样例反映当时前沿，不能代替今天的扩散模型全景。

Paper Verified。 论文声明目标是统一理论框架、解释与其他深度生成模型的联系，再按任务、条件、架构和数据集整理视觉扩散方法。它没有训练一个统一模型，也没有进行新的横向实验。
页面页眉异常。 arXiv PDF 的 IEEE 模板页眉写着 “VOL. 14, NO. 8, AUGUST 2022”，与 Crossref 正式书目不一致。本页采用 DOI 元数据中的卷期页码，不把模板页眉当作出版事实。

研究动机与真正缺口

扩散模型在图像生成上同时展现高质量与高多样性，但理论入口分散在离散概率模型、score matching 和随机微分方程三套术语里；视觉应用也已从无条件生成扩展到编辑、反问题、医学和视频。

问题

同一种生成思想，三套表述

DDPM 预测噪声，NCSN 估计对数密度梯度，SDE 用连续时间随机过程统一前两者。若只记网络结构或采样公式，很难理解它们为何相通。

价值

把方法放回任务与条件

作者以任务、denoising condition、architecture、dataset 四列整理文献，帮助读者辨认“扩散模型”这个大类中实际解决的问题和所依赖的信息。

论文 Figure 1，逐年扩散模型论文数量统计
Figure 1。 作者按 Google Scholar 搜索结果粗略统计扩散模型论文数量。图中 2022 年为当年早期统计，属于趋势示意；论文没有给出可复核的检索式、去重流程与完整样本清单。
Our Interpretation。 这篇综述最持久的贡献是“翻译层”：它把噪声预测、score estimation 与 reverse-time dynamics 解释为同一概率过程的不同参数化。文献表的时效性会快速下降，理论坐标系依旧可用于阅读后续工作。

问题形式与符号

\(x_0\)：真实数据或原始图像，服从未知数据分布 \(p(x_0)\)。
\(x_t\)：第 \(t\) 个噪声水平的样本；\(x_T\) 应接近标准高斯噪声。
\(T\)：离散扩散步数。经典 DDPM 示例采用 \(T=1000\)。
\(\beta_t\)：第 \(t\) 步加入噪声的方差，\(\alpha_t=1-\beta_t\)。
\(\widehat{\beta}_t\)：论文记号，定义为 \(\prod_{i=1}^{t}\alpha_i\)；许多现代文献把同一个量写作 \(\bar{\alpha}_t\)。
\(z_t\)：标准高斯噪声；\(z_{\theta}(x_t,t)\) 是神经网络的噪声估计。
\(s_{\theta}(x,t)\)：score network，逼近 \(\nabla_x\log p_t(x)\)。
\(f,\sigma\)：连续 SDE 的 drift 与 diffusion coefficient。

离散前向 Markov 过程：

\[p(x_t\mid x_{t-1})=\mathcal{N}\!\left(x_t;\sqrt{1-\beta_t}\,x_{t-1},\beta_t\mathbf{I}\right).\]

从 \(x_0\) 一步采样任意时刻：

\[x_t=\sqrt{\widehat{\beta}_t}\,x_0+\sqrt{1-\widehat{\beta}_t}\,z_t,\qquad z_t\sim\mathcal{N}(0,\mathbf{I}).\]

输入是干净训练图像与随机时间步；训练目标通常是恢复该步噪声或 score。推理输入是高斯噪声与可选条件，输出通过多步逆过程成为图像。条件可以是类别、文本、图像、mask、测量值、帧或 latent representation。

三种生成框架

论文 Figure 3，DDPM、NCSN 与 SDE 的统一框架
Figure 3。 原论文的统一示意：三种框架都让数据逐渐走向噪声，再学习逆向回到数据；差别主要在时间离散方式、学习对象与数值采样方法。

DDPM：学习每一步的逆高斯转移

当每个 \(\beta_t\) 很小且 \(\widehat{\beta}_T\rightarrow0\) 时，末态接近高斯，逆转移也可用高斯建模。网络接收 \(x_t\) 和时间嵌入，原始形式预测均值与协方差；Ho 等固定协方差并改为预测噪声。

\[\mathcal{L}_{\mathrm{vlb}}=-\log p_{\theta}(x_0\mid x_1)+\mathrm{KL}\!\left(p(x_T\mid x_0)\mathbin\Vert\pi(x_T)\right)+\sum_{t=2}^{T}\mathrm{KL}\!\left(p(x_{t-1}\mid x_t,x_0)\mathbin\Vert p_{\theta}(x_{t-1}\mid x_t)\right).\]\[\mu_{\theta}(x_t,t)=\frac{1}{\sqrt{\alpha_t}}\left(x_t-\frac{1-\alpha_t}{\sqrt{1-\widehat{\beta}_t}}z_{\theta}(x_t,t)\right).\]\[\mathcal{L}_{\mathrm{simple}}=\mathbb{E}_{t,x_0,z_t}\!\left[\left\lVert z_t-z_{\theta}(x_t,t)\right\rVert_2^2\right].\]

上式的 ELBO 分解省略了外层记号；严格训练目标还要对 \(x_0\sim p_{\mathrm{data}}(x_0)\) 以及完整前向轨迹 \(x_{1:T}\sim q(x_{1:T}\mid x_0)\) 取期望。第一项是该期望下的重建负对数似然，末态 KL 让前向终点匹配先验，中间 KL 让学习到的逆转移接近已知前向 posterior。简化损失舍弃时间相关权重，使每个采样到的时间步直接做噪声回归。

采样 \(x_T\sim\mathcal{N}(0,\mathbf{I})\)。
从 \(t=T\) 到 \(1\)，用网络估计 \(z_{\theta}(x_t,t)\) 并计算均值。
当 \(t\gt1\) 时加入 \(\sigma_t z\)；最终一步令随机项为零，得到 \(x_0\)。

NCSN：学习多噪声尺度的 score

score \(\nabla_x\log p(x)\) 指向高密度方向。原始 score matching 需要未知真 score；denoising score matching 先用已知高斯扰动构造条件 score，再训练单个网络覆盖一组噪声尺度。

\[x_i=x_{i-1}+\frac{\gamma}{2}\nabla_x\log p(x)+\sqrt{\gamma}\,\omega_i.\]\[\nabla_{x_t}\log p_{\sigma_t}(x_t\mid x)=-\frac{x_t-x}{\sigma_t^2}.\]\[\mathcal{L}_{\mathrm{dsm}}=\frac{1}{T}\sum_{t=1}^{T}\lambda(\sigma_t)\,\mathbb{E}\!\left[\left\lVert s_{\theta}(x_t,\sigma_t)+\frac{x_t-x}{\sigma_t^2}\right\rVert_2^2\right].\]

推理采用 annealed Langevin dynamics：从最大噪声尺度开始，在每一尺度执行 \(N\) 次带随机扰动的 score 更新，再把结果传给下一尺度。噪声项帮助离开局部区域，逐级退火让采样从平滑密度走向数据流形。

SDE：连续时间统一

前向过程由 drift 逐渐消除信号，diffusion term 注入布朗噪声；逆时间 SDE 的额外项由 score 决定。因此，只要学到所有时间的 score，就能用数值 SDE solver 从噪声积分回数据。

\[\mathrm{d}x=f(x,t)\,\mathrm{d}t+\sigma(t)\,\mathrm{d}\omega.\]\[\mathrm{d}x=\left[f(x,t)-\sigma(t)^2\nabla_x\log p_t(x)\right]\mathrm{d}t+\sigma(t)\,\mathrm{d}\widehat{\omega}.\]\[\mathcal{L}_{\mathrm{dsm}}^{\ast}=\mathbb{E}_{t}\!\left[\lambda(t)\mathbb{E}_{x_0,x_t}\!\left[\left\lVert s_{\theta}(x_t,t)-\nabla_{x_t}\log p_t(x_t\mid x_0)\right\rVert_2^2\right]\right].\]

Algorithm 3 从 \(t=T\) 走向 \(0\)，所以离散时间增量 \(\Delta t\lt0\)。Euler–Maruyama 的 reverse update 必须对布朗增量使用 \(\sqrt{\lvert\Delta t\rvert}\,z\)，不能把负时间步直接放进平方根：

\[x_{t+\Delta t}=x_t+\left[f(x_t,t)-\sigma(t)^2s_{\theta}(x_t,t)\right]\Delta t+\sigma(t)\sqrt{\lvert\Delta t\rvert}\,z,\quad z\sim\mathcal{N}(0,\mathbf{I}),\quad\Delta t\lt0.\]

离散 DDPM 可对应 variance-preserving SDE，NCSN 的噪声扰动可对应 variance-exploding SDE。论文还指出 reverse SDE 有对应的 probability flow ODE：

\[\mathrm{d}x=\left[f(x,t)-\frac{1}{2}\sigma(t)^2\nabla_x\log p_t(x)\right]\mathrm{d}t.\]

ODE 与 SDE 共享相同的边缘分布，提供确定性采样、可逆映射和通过瞬时变量替换计算 likelihood 的入口。该公式是统一视角的重要延伸；数值误差和网络 score 误差仍决定实际结果。

从 ELBO 到噪声回归

附录把 DDPM 训练的关键化简完整串联起来。理解这段推导可以避免把 “预测噪声” 当作经验技巧。

引入整个噪声轨迹。 把 \(x_{1:T}\) 看成 latent variables，将 \(\log p_{\theta}(x_0)\) 写成联合分布的边缘化。
应用 Jensen 不等式。 得到负对数似然的可优化上界，期望分布由已知的前向过程给出。
利用 Markov 分解。 前向概率写成 \(\prod_t p(x_t\mid x_{t-1})\)，逆向联合概率写成 \(p(x_T)\prod_t p_{\theta}(x_{t-1}\mid x_t)\)。
条件化使 posterior 可解。 \(p(x_{t-1}\mid x_t)\) 难求，但给定 \(x_0\) 后的 \(p(x_{t-1}\mid x_t,x_0)\) 是高斯。
固定协方差。 中间 KL 变成两个均值之间的加权平方距离。
重参数化均值。 真实 posterior mean 与模型 mean 都可写为 \(x_t\) 减去噪声项；它们的距离等价于真实噪声与预测噪声的距离。
\[\mathcal{L}_{\mathrm{kl}}=\frac{\beta_t^2}{2\sigma_t^2\alpha_t(1-\widehat{\beta}_t)}\left\lVert z_t-z_{\theta}(x_t,t)\right\rVert_2^2.\]
Our Interpretation。 \(\mathcal{L}_{\mathrm{simple}}\) 进一步删除上式的时间权重。它继承 ELBO 的结构来源，同时不再等同于原始加权变分目标。采样质量变好属于 Ho 等原始工作的经验发现，这篇综述负责解释关系，没有重新做消融。

与其他生成模型的关系

模型族共同点关键差异与联系
VAE都有 latent variables，并通过变分下界处理不可解的边缘似然。DDPM 的 latent 是一整条固定前向噪声轨迹；encoder 不需要学习。逆过程可视为层数很深且参数共享的 hierarchical VAE。
GAN都能从简单先验生成高维图像。GAN 以 adversarial game 训练并一次前向生成；扩散训练更稳定、mode coverage 通常更好，推理需要多步。综述引用当时结果说明扩散已在部分图像生成指标超越 GAN，未进行统一重测。
Energy-based modelscore 是能量梯度的相反数：若 \(p(x)\propto e^{-E(x)}\)，则 \(\nabla_x\log p(x)=-\nabla_xE(x)\)。NCSN 直接学习不同噪声尺度的 score，绕开归一化常数；Langevin dynamics 用该向量场采样。
Autoregressive都可建模复杂分布，并可给出 likelihood 相关目标。autoregressive 依照固定变量顺序生成，带来单向偏置；扩散同时更新整幅样本。离散扩散与 autoregressive transition 也可以组合。
Normalizing flow都连接简单先验与数据，并存在可逆连续动力学视角。flow 要求可逆变换与 Jacobian；probability flow ODE 提供确定性连续映射，但需要 score 和 ODE 积分。

训练、推理与系统设计

网络

DDPM backbone 的准确表述

综述正文把 Ho 等的网络概括为 PixelCNN++，但原始 DDPM 明确采用 U-Net 形状的 backbone，并以 Wide ResNet blocks、group normalization、self-attention 与 sinusoidal time embedding 构成。后续方法也采用 Transformer、VAE、GAN generator、NCSN++ 等架构，不能统一写成一种 U-Net。

DDPM 示例

固定 schedule

引用 Ho 等的设置：\(T=1000\)，\(\beta_t\) 从 \(10^{-4}\) 线性增加到 \(2\times10^{-2}\)。这属于原始 DDPM 示例，不能外推到表中所有方法。

采样

solver 决定成本

DDPM 逐步祖先采样，NCSN 每一噪声尺度执行多次 Langevin 更新，SDE 依赖 Euler-Maruyama 或 predictor-corrector 等数值 solver。

条件

guidance 与输入

类别、文本、图像、mask、测量或 frame 可进入 denoiser。classifier guidance 使用外部分类器梯度；classifier-free guidance 在同一模型中混合有条件和无条件 score。

加速

减少 network evaluations

综述覆盖 learned variance、DDIM、PNDM、知识蒸馏、bilateral schedule、latent diffusion 等方向。每种方法的步数和质量衡量协议不同。

复现边界

没有全局 recipe

论文没有统一 optimizer、learning rate、batch size、epoch、GPU 或训练时长，也没有公开统一代码。复现具体方法必须回到 Table 1 对应原论文。

Author Claim。 多步推理是主要缺点，GAN 仍更快；CLIP conditioning 可能继承拼写信息不足等问题。论文通过引用已有工作支撑这些判断，没有自行控制变量验证。
Paper vs. original implementation。 PixelCNN++ 是综述正文对 DDPM 网络来源的简写或误述；复现应依照 DDPM 原论文及代码的 U-Net / Wide ResNet 实现。分类表还包含 diffusion-GAN、GAN 初始化和 adversarial score matching 等混合方法，因此只有“无条件生成”子节的基础设定可称为无监督，不能把全部收录方法概括为无需 adversarial training。

采样加速：机制与数学区别

综述将采样成本视为主线问题。下面把正文提到的主要方案放在同一参照系中：它们分别改变方差、轨迹、数值积分、训练目标或表示空间。

Learned variance

学逆过程方差，允许更粗时间网格

Improved DDPM 让网络同时预测噪声和插值系数 \(v\)，在前向 posterior variance \(\widetilde{\beta}_t\) 与 \(\beta_t\) 之间插值：

\[\log\Sigma_{\theta}=v\log\beta_t+(1-v)\log\widetilde{\beta}_t,\qquad \mathcal{L}_{\mathrm{hybrid}}=\mathcal{L}_{\mathrm{simple}}+\lambda\mathcal{L}_{\mathrm{vlb}}.\]

均值继续依赖噪声预测，变分项为方差提供学习信号。论文综述转述其可将采样降到约 50 步；该数字属于 Nichol 与 Dhariwal 的具体模型和协议。

DDIM

非 Markov 前向族与确定性轨迹

DDIM 构造与 DDPM 具有相同训练边缘分布的非 Markov 过程，沿子序列采样。先由 \(x_t\) 估计干净样本：

\[\widehat{x}_0=\frac{x_t-\sqrt{1-\widehat{\beta}_t}\,z_{\theta}(x_t,t)}{\sqrt{\widehat{\beta}_t}},\]\[x_{t-1}=\sqrt{\widehat{\beta}_{t-1}}\widehat{x}_0+\sqrt{1-\widehat{\beta}_{t-1}-\sigma_t^2}\,z_{\theta}(x_t,t)+\sigma_t z.\]

当 \(\sigma_t=0\) 时，给定初始噪声后的轨迹是确定性的；增加 \(\sigma_t\) 恢复随机性。它复用已训练的噪声网络，速度来自跳过时间点。

PNDM 与 solver

把采样看成在流形上的数值积分

PNDM 不重新训练 denoiser，先用 pseudo Runge–Kutta 建立高阶历史，再用 pseudo linear multi-step / Adams–Bashforth 组合最近的噪声预测。抽象地，更新可写为：

\[x_{t-\Delta t}=\Phi\!\left(x_t,\,z_{\theta,t},\,z_{\theta,t-\Delta t},\,z_{\theta,t-2\Delta t},\ldots\right).\]

与 DDIM 主要改变概率轨迹不同，PNDM 主要改进离散数值方法，用历史斜率提高少步积分精度；SDE 工作还覆盖 Euler–Maruyama、predictor-corrector 和 ODE solver。

Distillation

让学生一次更新拟合教师多次更新

Progressive distillation 生成教师两步轨迹的终点，训练学生用一次去噪到达同一点，然后反复把步数减半。若教师映射为 \(F_{\theta}\)，一轮目标可概括为：

\[\mathcal{L}_{\mathrm{distill}}=\mathbb{E}\!\left[\left\lVert F_{\psi}^{(1)}(x_t,t)-F_{\theta}^{(2)}(x_t,t)\right\rVert_2^2\right].\]

速度来自把计算迁移到训练阶段；学生误差会随多轮蒸馏累积，需要质量与步数之间的重新校准。

Latent diffusion

在压缩表示中完成前向与逆向过程

autoencoder 先将图像编码为 \(z_0=\mathcal{E}(x)\)，扩散模型在低维 \(z_t\) 上学习噪声，再由 \(\mathcal{D}(z_0)\) 解码。条件 \(c\) 通过 cross-attention 或拼接进入 denoiser：

\[\mathcal{L}_{\mathrm{LDM}}=\mathbb{E}_{z_0,c,t,\epsilon}\!\left[\left\lVert\epsilon-\epsilon_{\theta}(z_t,t,c)\right\rVert_2^2\right],\qquad z_0=\mathcal{E}(x).\]

它减少每一步的空间计算量，同时引入 autoencoder 重建误差与 latent bottleneck。综述还收录 discrete VAE / VQ 表示、D2C 与 latent score model，不能把所有 latent 方法视为同一个架构。

Guidance、反问题与编辑条件

Classifier guidance

当分类器 \(p_{\phi}(y\mid x_t,t)\) 精确且校准良好时，Bayes rule 给出 \(s=1\) 的理想条件 score 恒等式：

\[\nabla_{x_t}\log p(x_t\mid y)=\nabla_{x_t}\log p(x_t)+\nabla_{x_t}\log p_{\phi}(y\mid x_t,t).\]

实际 classifier guidance 引入 guidance scale \(s\)，把学习到的 unconditional score \(s_{\theta}(x_t,t)\) 改成：

\[\widehat{s}_{\mathrm{guided}}(x_t,t,y)=s_{\theta}(x_t,t)+s\,\nabla_{x_t}\log p_{\phi}(y\mid x_t,t).\]

当 \(s\ne1\) 时，该向量场对应按 \(p_t(x_t)p_{\phi}(y\mid x_t,t)^s\) 重新加权的 tempered density，不能与真实条件 score 直接等同。更大的 \(s\) 通常提高条件一致性，同时可能降低多样性；外部分类器带来额外训练和推理成本。

Classifier-free guidance

同一网络在训练时随机丢弃条件，学到有条件与无条件预测；推理时对两者作线性外推：

\[\epsilon_{\mathrm{cfg}}=\epsilon_{\theta}(x_t,t,\varnothing)+w\left[\epsilon_{\theta}(x_t,t,c)-\epsilon_{\theta}(x_t,t,\varnothing)\right].\]

\(c\) 可以是类别或文本，\(\varnothing\) 表示空条件，\(w\) 是 guidance scale。它省去单独分类器，但每一步通常需要两次网络预测。

观测条件如何进入逆过程

方法条件机制结果与控制量
Posterior / inverse guidance给定测量 \(y=\mathcal{A}(x)+n\)，把 prior score 与 likelihood gradient 组合：\(\nabla_x\log p(x\mid y)=\nabla_x\log p(x)+\nabla_x\log p(y\mid x)\)。算子 \(\mathcal{A}\)、噪声模型和梯度近似决定 data consistency；用于 MRI、deblurring、super-resolution 等。
SDEdit把输入图像先扩散到中间时刻 \(t_0\)，再从该状态执行 reverse SDE。\(t_0\) 控制保留输入结构与服从生成 prior 的强弱；条件通过起点进入。
ILVR每一步用参考图像的当前噪声版本替换生成样本的低频分量。低通算子决定保留的布局尺度，无需重新训练基础扩散模型。
RePaint / masked editing已知区域从原图对应的前向噪声分布取样，未知区域由逆过程生成，并通过 forward/backward resampling 改善边界语义。mask 确定硬约束区域；重采样次数增加协调能力与计算量。
Text / CLIP guidance文本编码通过 cross-attention、classifier-free prediction 或 CLIP 相似度梯度影响 denoising。文本一致性、图像保真与多样性之间存在 guidance trade-off。

视觉任务谱系

论文 Figure 2，Stable Diffusion 生成样例
Figure 2。 论文通过 DreamStudio 生成的 Stable Diffusion 样例，展示当时 text-to-image 的条件生成能力。它是定性插图，没有固定随机种子、prompt 重复次数、失败样本或量化比较。

生成与条件控制

无条件图像生成、类别条件生成、text-to-image、few-shot generation，以及多条件控制。

图像变换与编辑

image-to-image translation、super-resolution、editing、inpainting、restoration、registration 与 counterfactual explanation。

理解与反问题

segmentation、classification、adversarial purification、MRI reconstruction、compressive sensing 等。

医学影像

generation、translation、segmentation 与 anomaly detection；条件常来自图像或测量。

时空与三维

video generation / infilling、point cloud generation、shape generation 与 completion。

多任务模型

同一扩散体系覆盖生成、修复、转换或 latent editing，表明 denoising prior 可被不同观测约束复用。

原论文 Table 1 · 完整分类

下表重建原文连续三页的全部方法行与五列信息。它是一张文献分类表，颜色只服务于原论文的任务分组；本页用实时筛选替代颜色编码。

Table 1 · 第 1 部分

论文 任务 去噪条件 架构 数据集
Austin  [78] image generation unconditional D3PM CIFAR-10
Bao  [20] image generation unconditional DDIM, Improved DDPM CelebA, ImageNet, LSUN Bedroom, CIFAR-10
Benny  [79] image generation unconditional DDPM, DDIM CIFAR-10, ImageNet, CelebA
Bond-Taylor  [80] image generation unconditional DDPM LSUN Bedroom, LSUN Church, FFHQ
Choi  [81] image generation unconditional DDPM FFHQ, AFHQ-Dog, CUB, MetFaces
De  [82] image generation unconditional DSB MNIST, CelebA
Deasy  [83] image generation unconditional NCSN MNIST, Fashion-MNIST, CIFAR-10, CelebA
Deja  [84] image generation unconditional Improved DDPM Fashion-MNIST, CIFAR-10, CelebA
Dockhorn  [21] image generation unconditional NCSN++, DDPM++ CIFAR-10
Ho  [2] image generation unconditional DDPM CIFAR-10, CelebA-HQ, LSUN
Huang  [59] image generation unconditional DDPM CIFAR-10, MNIST
Jing  [30] image generation unconditional NCSN++, DDPM++ CIFAR-10, CelebA-256-HQ, LSUN Church
Jolicoeur  [85] image generation unconditional NCSN CIFAR-10, LSUN Church, Stacked-MNIST
Jolicoeur  [86] image generation unconditional DDPM++, NCSN++ CIFAR-10, LSUN Church, FFHQ
Kim  [87] image generation unconditional NCSN++, DDPM++ CIFAR-10, CelebA, MNIST
Kingma  [88] image generation unconditional DDPM CIFAR-10, ImageNet
Kong  [89] image generation unconditional DDIM, DDPM LSUN Bedroom, CelebA, CIFAR-10
Lam  [90] image generation unconditional BDDM CIFAR-10, CelebA
Liu  [91] image generation unconditional PNDM CIFAR-10, CelebA
Ma  [92] image generation unconditional NCSN, NCSN++ CIFAR-10, CelebA, LSUN Bedroom, LSUN Church, FFHQ
Nachmani  [93] image generation unconditional DDIM, DDPM CelebA, LSUN Church
Nichol  [6] image generation unconditional DDPM CIFAR-10, ImageNet
Pandey  [19] image generation unconditional DDPM CelebA-HQ, CIFAR-10
San  [94] image generation unconditional DDPM CelebA, LSUN Bedroom, LSUN Church
Sehwag  [95] image generation unconditional ADM CIFAR-10, ImageNet
Sohl-Dickstein  [1] image generation unconditional DDPM MNIST, CIFAR-10, Dead Leaf Images
Song  [13] image generation unconditional NCSN FFHQ, CelebA, LSUN Bedroom, LSUN Tower, LSUN Church Outdoor
Song  [15] image generation unconditional DDPM++ CIFAR-10, ImageNet 32\(\times\)32
Song  [7] image generation unconditional DDIM CIFAR-10, CelebA, LSUN
Vahdat  [17] image generation unconditional NCSN++ CIFAR-10, CelebA-HQ, MNIST
Wang  [96] image generation unconditional DDIM CIFAR-10, CelebA
Wang  [97] image generation unconditional StyleGAN2, ProjectedGAN CIFAR-10, STL-10, LSUN Bedroom, LSUN Church, AFHQ, FFHQ
Watson  [98] image generation unconditional DDPM CIFAR-10, ImageNet
Watson  [8] image generation unconditional Improved DDPM CIFAR-10, ImageNet 64\(\times\)64
Xiao  [99] image generation unconditional NCSN++ CIFAR-10
Zhang  [71] image generation unconditional DDPM CIFAR-10, MNIST
Zheng  [100] image generation unconditional DDPM CIFAR-10, CelebA, CelebA-HQ, LSUN Bedroom, LSUN Church
Bordes  [101] conditional image generation conditioned on latent representations Improved DDPM ImageNet
Campbell  [102] conditional image generation unconditional, conditioned on sound DDPM CIFAR-10, Lakh Pianoroll
Chao  [103] conditional image generation conditioned on class Score SDE, Improved DDPM CIFAR-10, CIFAR-100
Dhariwal  [5] conditional image generation unconditional, classifier guidance ADM LSUN Bedroom, LSUN Horse, LSUN Cat

Table 1 · 第 2 部分

论文任务去噪条件架构数据集
Ho  [104] conditional image generation conditioned on label DDPM LSUN, ImageNet
Ho  [77] conditional image generation unconditional, classifier-free guidance ADM ImageNet 64\(\times\)64, ImageNet 128\(\times\)128
Karras  [105] conditional image generation unconditional, conditioned on class DDPM++, NCSN++, DDPM, DDIM CIFAR-10, ImageNet 64\(\times\)64
Liu  [106] conditional image generation conditioned on text, image, style guidance DDPM FFHQ, LSUN Cat, LSUN Horse, LSUN Bedroom
Liu  [22] conditional image generation conditioned on text, 2D positions, relational descriptions between items, human facial attributes Improved DDPM CLEVR, Relational CLEVR, FFHQ
Lu  [107] conditional image generation unconditional, conditioned on class DDIM CIFAR-10, CelebA, ImageNet, LSUN Bedroom
Salimans  [108] conditional image generation unconditional, conditioned on class DDIM CIFAR-10, ImageNet, LSUN
Singh  [109] conditional image generation conditioned on noise DDIM ImageNet
Sinha  [16] conditional image generation unconditional, conditioned on label D2C CIFAR-10, CIFAR-100, fMoW, CelebA-64, CelebA-HQ-256, FFHQ-256
Ho  [34] image-to-image translation conditioned on image Improved DDPM ctest10k, places10k
Li  [37] image-to-image translation conditioned on image DDPM Face2Comic, Edges2Shoes, Edges2Handbags
Sasaki  [110] image-to-image translation conditioned on image DDPM CMP Facades, KAIST Multispectral Pedestrian
Wang  [36] image-to-image translation conditioned on image DDIM ADE20K, COCO-Stuff, DIODE
Wolleb  [38] image-to-image translation conditioned on image Improved DDPM BRATS
Zhao  [35] image-to-image translation conditioned on image DDPM CelebaA-HQ, AFHQ
Gu  [111] text-to-image generation conditioned on text VQ-Diffusion CUB-200, Oxford 102 Flowers, MS-COCO
Jiang  [23] text-to-image generation conditioned on text Transformer-based encoder-decoder DeepFashion-MultiModal
Ramesh  [112] text-to-image generation conditioned on text ADM MS-COCO, AVA
Rombach  [11] text-to-image generation conditioned on text LDM OpenImages, WikiArt, LAION-2B-en, ArtBench
Saharia  [12] text-to-image generation conditioned on text Imagen MS-COCO, DrawBench
Shi  [9] text-to-image generation unconditional, conditioned on text Improved DDPM Conceptual Captions, MS-COCO
Zhang  [113] text-to-image generation unconditional, conditioned on text DDIM CIFAR-10, CelebA, ImageNet
Daniels  [25] super-resolution conditioned on image NCSN CIFAR-10, CelebA
Saharia  [18] super-resolution conditioned on image DDPM++ FFHQ, CelebA-HQ, ImageNet-1K
Avrahami  [114] image editing conditioned on image and mask DDPM, ADM ImageNet, CUB, LSUN Bedroom, MS-COCO
Avrahami  [31] region image editing text guidance DDPM PaintByWord
Meng  [33] image editing conditioned on image Score SDE, DDPM, Improved DDPM LSUN, CelebA-HQ
Lugmayr  [29] inpainting unconditional DDPM CelebA-HQ, ImageNet
Nichol  [14] inpainting conditioned on image, text guidance ADM MS-COCO
Amit  [42] image segmentation conditioned on image Improved DDPM Cityscapes, Vaihingen, MoNuSeg
Baranchuk  [39] image segmentation conditioned on image Improved DDPM LSUN, FFHQ-256, ADE-Bedroom-30, CelebA-19
Batzolis  [24] multi-task (inpainting, super-resolution, edge-to-image) conditioned on image DDPM CelebA, Edges2Shoes
Batzolis  [115] multi-task (image generation, super-resolution, inpainting, image-to-image translation) unconditional DDIM ImageNet, CelebA-HQ, CelebA, Edges2Shoes
Blattmann  [116] multi-task (image generation) unconditional, conditioned on text, class LDM ImageNet
Choi  [32] multi-task (image generation, image-to-image translation, image editing) conditioned on image DDPM FFHQ, MetFaces
Chung  [26] multi-task (inpainting, super-resolution, MRI reconstruction) conditioned on image CCDF FFHQ, AFHQ, fastMRI knee
Esser  [28] multi-task (image generation, inpainting) unconditional, conditioned on class, image and text ImageBART ImageNet, Conceptual Captions, FFHQ, LSUN
Gao  [117] multi-task (image generation, inpainting) unconditional, conditioned on image DDPM CIFAR-10, LSUN, CelebA
Graikos  [40] multi-task (image generation, image segmentation) conditioned on class DDIM FFHQ-256, CelebA

Table 1 · 第 3 部分

论文任务去噪条件架构数据集
Hu  [118] multi-task (image generation, inpainting) unconditional, conditioned on image VQ-DDM CelebA-HQ, LSUN Church
Khrulkov  [119] multi-task (image generation, image-to-image translation) conditioned on class Improved DDPM AFHQ, FFHQ, MetFaces, ImageNet
Kim  [120] multi-task (image translation, multi-attribute transfer) conditioned on image, portrait, stroke DDIM ImageNet, CelebA-HQ, AFHQ-Dog, LSUN Bedroom, Church
Luo  [121] multi-task (point cloud generation, auto-encoding, unsupervised representation learning) conditioned on shape latent DDPM ShapeNet
Lyu  [122] multi-task (image generation, image editing) unconditional, conditioned on class DDPM CIFAR-10, CelebA, ImageNet, LSUN Bedroom, LSUN Cat
Preechakul  [123] multi-task (latent interpolation, attribute manipulation) conditioned on latent representation DDIM CelebA-HQ
Rombach  [10] multi-task (super-resolution, image generation, inpainting) unconditional, conditioned on image VQ-DDM ImageNet, CelebA-HQ, FFHQ, LSUN
Shi  [124] multi-task (super-resolution, inpainting) conditioned on image Improved DDPM MNIST, CelebA
Song  [3] multi-task (image generation, inpainting) unconditional, conditioned on image NCSN MNIST, CIFAR-10, CelebA
Kadkhodaie  [125] multi-task (Spatial super-resolution, Deblurring, Compressive sensing, Inpainting, Random missing pixels) conditioned on linear measurements BF-CNN MNIST, Set5, Set68, Set14
Song  [4] multi-task (image generation, inpainting, colorization) unconditional, conditioned on image, class NCSN++, DDPM++ CelebA-HQ, CIFAR-10, LSUN
Hu  [126] medical image-to-image translation conditioned on image DDPM ONH
Chung  [127] medical image generation conditioned on measurements NCSN++ fastMRI knee
Özbey  [128] medical image generation conditioned on image Improved DDPM IXI, Gold Atlas - Male Pelvis
Song  [129] medical image generation conditioned on measurements NCSN++ LIDC, LDCT Image and Projection, BRATS
Wolleb  [41] medical image segmentation conditioned on image Improved DDPM BRATS
Sanchez  [130] medical image segmentation and anomaly detection conditioned on image and binary variable ADM BRATS
Pinaya  [44] medical image segmentation and anomaly detection conditioned on image DDPM MedNIST, UK Biobank Images, WMH, BRATS, MSLUB
Wolleb  [45] medical image anomaly detection conditioned on image DDIM CheXpert, BRATS
Wyatt  [46] medical image anomaly detection conditioned on image ADM NFBS, 22 MRI scans
Harvey  [131] video generation conditioned on frames FDM GQN-Mazes, MineRL Navigate, CARLA Town01
Ho  [132] video generation unconditional, conditioned on text DDPM 101 Human Actions
Yang  [133] video generation conditioned on video representation RVD BAIR, KTH Actions, Simulation, Cityscapes
Höppe  [134] video generation and infilling conditioned on frames RaMViD BAIR, Kinetics-600, UCF-101
Giannone  [135] few-shot image generation conditioned on image Improved DDPM CIFAR-FS, mini-ImageNet, CelebA
Jeanneret  [136] counterfactual explanations unconditional DDPM CelebA
Sanchez  [137] counterfactual estimates conditional ADM MNIST, ImageNet
Kawar  [27] image restoration conditioned on image DDIM FFHQ, ImageNet
Özdenizci  [138] image restoration conditioned on image DDPM Snow100K, Outdoor-Rain, RainDrop
Kim  [139] image registration conditioned on image DDPM Radboud Faces, OASIS-3
Nie  [140] adversarial purification conditioned on image Score SDE, Improved DDPM, DDIM CIFAR-10, ImageNet, CelebA-HQ
Wang  [141] semantic image generation conditioned on semantic map DDPM Cityscapes, ADE20K, CelebAMask-HQ
Zhou  [142] shape generation and completion unconditional, conditional shape completion DDPM ShapeNet, PartNet
Zimmermann  [43] classification conditioned on label DDPM++ CIFAR-10
如何阅读。 同一架构名称并不保证训练设置相同；同一数据集也可能使用不同分辨率、样本数和评价协议。该表适合定位原论文，不能直接充当公平性能排行榜。

实验、评价与证据边界

综述自己的实验

没有统一 benchmark

作者没有重新训练表中模型，没有公开复现实验、统计显著性或统一 sample budget。Figure 2 是作者通过 DreamStudio 生成的定性样例；Figure 1 是粗略文献数量统计。

引用结果

跨论文数字不可直接排序

正文综述 FID、IS、NLL、precision / recall 等已有结果，也讨论采样步数，但不同论文在数据预处理、分辨率、sample count、classifier 和 checkpoint 上存在差异。

评价指标如何解释

指标测量内容综述阅读时的限制
FID生成与真实特征分布的均值、协方差距离，较低更好。对 sample count、特征提取器和数据预处理敏感；不同论文报告值缺少统一复算。
Inception Score偏好单样本类别明确且整体类别分布多样。不直接比较真实分布，依赖 ImageNet classifier。
NLL / bits-per-dim概率模型对数据的 likelihood。高 likelihood 不必然对应更佳感知质量；估计方法也可能不同。
Precision / Recall分别近似衡量 fidelity 与 coverage。特征空间与邻域定义影响结果；有助于揭示 FID 隐藏的 trade-off。
Network evaluations采样时调用 denoiser 的次数。单次网络大小与硬件速度仍不同，不能等同于真实延迟。
没有 ablation。 综述叙述其他论文的消融和结果，但本论文自身没有可拆除的模型组件，也没有训练一个新系统。因此不能把正文引用的性能变化写成本综述验证的因果结论。
Paper Verified。 论文明确指出采样步数、文本可读性、未充分探索的任务、判别 representation、视频长期依赖与 multi-purpose models 是重要限制或未来方向。

Reviewer Commentary

Strengths

理论解释具有长期价值

三框架统一顺序合理：先定义前向扰动，再说明学习对象和逆向采样。附录从边缘似然推导到噪声回归，能够支撑读者理解 DDPM 的训练目标。

Table 1 同时保留任务、条件、架构与数据集，信息密度高，避免仅按论文年代罗列。

Weaknesses

范围和证据透明度有限

检索协议、纳入排除标准、搜索数据库和质量评估没有形成系统综述式流程，因此“comprehensive”难以严格复核。

正文跨论文转述性能时，sample count、评估实现与训练预算缺少统一标准；分类表也没有 venue、年份、代码状态或核心数值列。

Reproducibility

可复现的是理论入口

核心公式和三套算法足以重建基础 sampler 的逻辑。具体论文的 optimizer、网络细节、数据 split、采样超参数与评价代码仍需回到引用文献。

Figure 1 的统计不能复算；Figure 2 的 DreamStudio 生成没有公开 seed 与完整生成记录。

Potential Improvements

面向持续更新的证据表

后续综述可预注册检索式，公开结构化文献数据库，为每个结果记录数据版本、分辨率、样本数、NFE、硬件延迟和代码提交，并把理论 taxonomy 与可复现实验分开维护。

对基础理论可增加 \(v\)-prediction、EDM parameterization、flow matching 与现代 solver 的符号转换图。

Research Extension。 对 procedural material generation，可将可执行 material graph 或渲染图作为结构条件，将 renderer 反馈写成 guidance 或 test-time reward；把拓扑有效性约束嵌入逆过程，并分别评价外观相似度、图有效率、可编辑性与实际执行成本。这是基于统一扩散视角提出的研究设计，原论文没有验证。

References

  1. Croitoru et al., Diffusion Models in Vision: A Survey：arXiv 版本历史、摘要、作者与正式 DOI。
  2. IEEE TPAMI DOI 记录：正式出版身份；卷期页码由 Crossref DOI 元数据交叉核对。
  3. Ho et al., Denoising Diffusion Probabilistic Models：DDPM、简化噪声预测目标与基础采样。
  4. Song and Ermon, Generative Modeling by Estimating Gradients of the Data Distribution：NCSN 与 annealed Langevin dynamics。
  5. Song et al., Score-Based Generative Modeling through Stochastic Differential Equations：reverse-time SDE 与 probability flow ODE。
  6. Song et al., Denoising Diffusion Implicit Models：非 Markov 前向过程与加速采样。
  7. Rombach et al., High-Resolution Image Synthesis with Latent Diffusion Models：latent diffusion 与文本条件生成。

原论文完整参考文献映射

Table 1 每一行的方括号编号都可跳转到下列完整引用；编号与论文参考文献顺序一致。

  1. J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli, “Deep unsupervised learning using non-equilibrium thermodynamics,” in Proceedings of ICML, pp. 2256–2265, 2015.
  2. J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” in Proceedings of NeurIPS, vol. 33, pp. 6840–6851, 2020.
  3. Y. Song and S. Ermon, “Generative modeling by estimating gradients of the data distribution,” in Proceedings of NeurIPS, vol. 32, pp. 11918–11930, 2019.
  4. Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole, “Score-Based Generative Modeling through Stochastic Differential Equations,” in Proceedings of ICLR, 2021.
  5. P. Dhariwal and A. Nichol, “Diffusion models beat GANs on image synthesis,” in Proceedings of NeurIPS, vol. 34, pp. 8780–8794, 2021.
  6. A. Q. Nichol and P. Dhariwal, “Improved denoising diffusion probabilistic models,” in Proceedings of ICML, pp. 8162–8171, 2021.
  7. J. Song, C. Meng, and S. Ermon, “Denoising Diffusion Implicit Models,” in Proceedings of ICLR, 2021.
  8. D. Watson, W. Chan, J. Ho, and M. Norouzi, “Learning fast samplers for diffusion models by differentiating through sample quality,” in Proceedings of ICLR, 2021.
  9. J. Shi, C. Wu, J. Liang, X. Liu, and N. Duan, “DiVAE: Photorealistic Images Synthesis with Denoising Diffusion Decoder,” arXiv preprint arXiv:2206.00386, 2022.
  10. R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer, “High-Resolution Image Synthesis with Latent Diffusion Models,” in Proceedings of CVPR, pp. 10684–10695, 2022.
  11. R. Rombach, A. Blattmann, and B. Ommer, “Text-Guided Synthesis of Artistic Images with Retrieval-Augmented Diffusion Models,” arXiv preprint arXiv:2207.13038, 2022.
  12. C. Saharia, W. Chan, S. Saxena, L. Li, J. Whang, E. Denton, S. K. S. Ghasemipour, B. K. Ayan, S. S. Mahdavi, R. G. Lopes, et al., “Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding,” arXiv preprint arXiv:2205.11487, 2022.
  13. Y. Song and S. Ermon, “Improved techniques for training score-based generative models,” in Proceedings of NeurIPS, vol. 33, pp. 12438–12448, 2020.
  14. A. Nichol, P. Dhariwal, A. Ramesh, P. Shyam, P. Mishkin, B. McGrew, I. Sutskever, and M. Chen, “GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models,” in Proceedings of ICML, pp. 16784–16804, 2021.
  15. Y. Song, C. Durkan, I. Murray, and S. Ermon, “Maximum likelihood training of score-based diffusion models,” in Proceedings of NeurIPS, vol. 34, pp. 1415–1428, 2021.
  16. A. Sinha, J. Song, C. Meng, and S. Ermon, “D2C: Diffusion-decoding models for few-shot conditional generation,” in Proceedings of NeurIPS, vol. 34, pp. 12533–12548, 2021.
  17. A. Vahdat, K. Kreis, and J. Kautz, “Score-based generative modeling in latent space,” in Proceedings of NeurIPS, vol. 34, pp. 11287–11302, 2021.
  18. C. Saharia, J. Ho, W. Chan, T. Salimans, D. J. Fleet, and M. Norouzi, “Image super-resolution via iterative refinement,” arXiv preprint arXiv:2104.07636, 2021.
  19. K. Pandey, A. Mukherjee, P. Rai, and A. Kumar, “VAEs meet diffusion models: Efficient and high-fidelity generation,” in Proceedings of NeurIPS Workshop on DGMs and Applications, 2021.
  20. F. Bao, C. Li, J. Zhu, and B. Zhang, “Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models,” in Proceedings of ICLR, 2022.
  21. T. Dockhorn, A. Vahdat, and K. Kreis, “Score-based generative modeling with critically-damped Langevin diffusion,” in Proceedings of ICLR, 2022.
  22. N. Liu, S. Li, Y. Du, A. Torralba, and J. B. Tenenbaum, “Compositional Visual Generation with Composable Diffusion Models,” in Proceedings of ECCV, 2022.
  23. Y. Jiang, S. Yang, H. Qiu, W. Wu, C. C. Loy, and Z. Liu, “Text2Human: Text-Driven Controllable Human Image Generation,” ACM Transactions on Graphics, vol. 41, no. 4, pp. 1–11, 2022.
  24. G. Batzolis, J. Stanczuk, C.-B. Schönlieb, and C. Etmann, “Conditional image generation with score-based diffusion models,” arXiv preprint arXiv:2111.13606, 2021.
  25. M. Daniels, T. Maunu, and P. Hand, “Score-based generative neural networks for large-scale optimal transport,” in Proceedings of NeurIPS, pp. 12955–12965, 2021.
  26. H. Chung, B. Sim, and J. C. Ye, “Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction,” in Proceedings of CVPR, pp. 12413–12422, 2022.
  27. B. Kawar, M. Elad, S. Ermon, and J. Song, “Denoising diffusion restoration models,” in Proceedings of DGM4HSD, 2022.
  28. P. Esser, R. Rombach, A. Blattmann, and B. Ommer, “ImageBART: Bidirectional Context with Multinomial Diffusion for Autoregressive Image Synthesis,” in Proceedings of NeurIPS, vol. 34, pp. 3518–3532, 2021.
  29. A. Lugmayr, M. Danelljan, A. Romero, F. Yu, R. Timofte, and L. Van Gool, “RePaint: Inpainting using Denoising Diffusion Probabilistic Models,” in Proceedings of CVPR, pp. 11461–11471, 2022.
  30. B. Jing, G. Corso, R. Berlinghieri, and T. Jaakkola, “Subspace diffusion generative models,” arXiv preprint arXiv:2205.01490, 2022.
  31. O. Avrahami, D. Lischinski, and O. Fried, “Blended diffusion for text-driven editing of natural images,” in Proceedings of CVPR, pp. 18208–18218, 2022.
  32. J. Choi, S. Kim, Y. Jeong, Y. Gwon, and S. Yoon, “ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models,” in Proceedings of ICCV, pp. 14347–14356, 2021.
  33. C. Meng, Y. Song, J. Song, J. Wu, J.-Y. Zhu, and S. Ermon, “SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations,” in Proceedings of ICLR, 2021.
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原论文 Figures 1–3 与完整 Table 1 均来自 arXiv v6 TeX source；阅读正文以本地 v5 PDF 为准，并逐行检查 v5/v6 差异。核查日期：2026-09-28。