扩散薛定谔桥和最优传输 - 知乎 (zhihu.com)

1 Introduction

1.1 Problem Statement

1.1.1 最优传输问题Optimal Transport(OT)

Problem 1 (Optimal Mass Transport). Suppose $(X,\mu ),(Y,v)$ are metric space with probabilities measures, which have the same total mass ${\int }_X\mu dx={\int }_Y\nu dy$. A map $T:X\to Y$ is measure preserving, if for any measurable set $B\subset Y,\mu (T^{-1}$ $(B))=v(B)$. Given a transportation cost function $c:X\times$ $Y\to \mathbb{R}$, find the measure preserving map $T:X\to Y$ that minimizes the total transportation cost

找到两个分布之间的一个变换使得这个移动成本最小。

1.2 Stated Contribution

2 Related Work

3 Method

4 Experiment

4.1 Implementation Details

5 Summary

5.1 Relative Position

6 Comments

7 DSB implementation analysis

https://github.com/checkcrab/SDSB/blob/main/util/runner.py

DSB会有backward_model和forward_model两个部分，分别放进两个独立的优化器中。

DSB自己实现了一个Noiser，负责创建样本x_0和样本x_1之间变换的每个时间步的取值组成的轨迹,噪音的轨迹，时间步的轨迹。