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<!DOCTYPE html>
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<title>扩散模型教程</title>
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<span class="tree-title">扩散模型教程</span>
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<span class="tree-title">第1章：扩散模型导论</span>
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<span class="tree-title">第3章：去噪扩散概率模型 (DDPM)</span>
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<span class="tree-title">第4章：基于分数的生成模型</span>
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<span class="tree-title">第5章：连续时间扩散模型 (PDE/SDE)</span>
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<span class="tree-title">第6章：流匹配 (Flow Matching)</span>
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<span class="tree-title">第11章：视频扩散模型</span>
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<span class="tree-title">附录C：信息几何与分数函数的力学解释</span>
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<article>
<h1 id="_1">扩散模型教程</h1>
<h2 id="diffusion-models-from-theory-to-practice">Diffusion Models: From Theory to Practice</h2>
<p>欢迎来到扩散模型教程！本教程将带你从基础理论逐步深入到实际应用，帮助你全面理解和掌握扩散模型这一强大的生成模型技术。</p>
<p>每个章节包含：</p>
<ul>
<li>理论基础与数学推导</li>
<li>可视化演示和交互式示例</li>
<li>编程练习与实践项目</li>
<li>习题与参考答案（默认折叠）</li>
</ul>
<h2 id="_2">前置知识要求</h2>
<p>本教程假设读者已具备以下基础知识：</p>
<ul>
<li><strong>概率论与统计</strong>：随机变量、概率分布、期望、方差、贝叶斯定理</li>
<li><strong>线性代数</strong>：矩阵运算、特征值分解、向量空间</li>
<li><strong>微积分</strong>：多元微积分、偏导数、链式法则、泰勒展开</li>
<li><strong>深度学习基础</strong>：神经网络、反向传播、卷积网络、Transformer</li>
<li><strong>PyTorch 编程</strong>：张量操作、自动微分、模型训练流程</li>
</ul>
<p>如果对某些概念不熟悉，建议先补充相关知识再开始学习。附录部分提供了部分高级数学概念的速成指南。</p>
<h2 id="_3">课程章节</h2>
<h3 id="1"><a href="chapter1.html">第1章：扩散模型导论</a></h3>
<p><em>已完成</em></p>
<p>介绍扩散模型的基本概念、历史发展、与其他生成模型的比较，以及前向扩散过程的数学基础。</p>
<h3 id="2u-netvit"><a href="chapter2.html">第2章：神经网络架构：U-Net与ViT</a></h3>
<p><em>已完成</em></p>
<p>探索去噪网络的历史发展，从医学图像分割到生成模型，深入理解U-Net架构演进和Vision Transformer的崛起。</p>
<h3 id="3-ddpm"><a href="chapter3.html">第3章：去噪扩散概率模型 (DDPM)</a></h3>
<p><em>已完成</em></p>
<p>深入理解DDPM的核心原理，包括前向过程、反向过程、变分下界推导、训练算法和完整实现。</p>
<h3 id="4"><a href="chapter4.html">第4章：基于分数的生成模型</a></h3>
<p><em>已完成</em></p>
<p>探索score matching和Langevin dynamics，理解扩散模型与分数函数的深层联系。</p>
<h3 id="5-pdesde"><a href="chapter5.html">第5章：连续时间扩散模型 (PDE/SDE)</a></h3>
<p><em>已完成</em></p>
<p>从随机微分方程(SDE)和偏微分方程(PDE)角度理解扩散模型，包括概率流ODE、Fokker-Planck方程等连续时间框架。</p>
<h3 id="6-flow-matching"><a href="chapter6.html">第6章：流匹配 (Flow Matching)</a></h3>
<p><em>已完成</em></p>
<p>连续正则化流、最优传输视角、与扩散模型的联系。</p>
<h3 id="7transformer-dit"><a href="chapter7.html">第7章：扩散Transformer (DiT)</a></h3>
<p><em>已完成</em></p>
<p>Diffusion Transformer架构、与U-Net的对比、可扩展性分析。</p>
<h3 id="8"><a href="chapter8.html">第8章：采样算法与加速技术</a></h3>
<p><em>已完成</em></p>
<p>学习DDIM、DPM-Solver等快速采样方法，以及如何优化生成质量与速度的平衡。</p>
<h3 id="9"><a href="chapter9.html">第9章：条件生成与引导技术</a></h3>
<p><em>已完成</em></p>
<p>掌握classifier guidance、classifier-free guidance等条件生成技术，实现可控生成。</p>
<h3 id="10-ldm"><a href="chapter10.html">第10章：潜在扩散模型 (LDM)</a></h3>
<p><em>已完成</em></p>
<p>理解Stable Diffusion的架构，学习如何在潜在空间中进行高效的扩散建模。</p>
<h3 id="11"><a href="chapter11.html">第11章：视频扩散模型</a></h3>
<p><em>已完成</em></p>
<p>时序建模、3D U-Net、视频生成的挑战与方法。</p>
<h3 id="12"><a href="chapter12.html">第12章：文本扩散模型</a></h3>
<p><em>已完成</em></p>
<p>探索离散域上的扩散模型，包括D3PM、Diffusion-LM等文本生成方法，以及embedding空间的扩散技术。</p>
<h3 id="13"><a href="chapter13.html">第13章：扩散模型的应用</a></h3>
<p><em>已完成</em></p>
<p>探索图像生成、图像编辑、超分辨率、3D生成等实际应用场景。</p>
<h3 id="14"><a href="chapter14.html">第14章：前沿研究与未来方向</a></h3>
<p><em>已完成</em></p>
<p>了解最新研究进展，包括一致性模型、扩散模型的未来发展趋势。</p>
<h2 id="_4">附录</h2>
<h3 id="a"><a href="appendix-a.html">附录A：测度论与随机过程速成</a></h3>
<p><em>已完成</em></p>
<p>为第5章PDE/SDE内容提供数学基础，包括σ-代数、测度、布朗运动等核心概念。</p>
<h3 id="b-bsde"><a href="appendix-b.html">附录B：倒向随机微分方程 (BSDE) 速成</a></h3>
<p><em>已完成</em></p>
<p>理解扩散模型反向过程的数学工具，包括BSDE基本理论、Feynman-Kac公式等。</p>
<h3 id="c"><a href="appendix-c.html">附录C：信息几何与分数函数的力学解释</a></h3>
<p><em>已完成</em></p>
<p>从信息几何角度理解扩散模型，揭示分数函数作为"力"的物理意义，建立与能量优化的联系。</p>
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