---
title: "前向扩散得分精度不能保证扩散采样的数值稳定性"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.08757v1"
permalink: "https://feed.astralor.com/items/itm_b9050a5597b829187d93e38a"
published: "2026-07-09T17:55:52.000Z"
score: 79
channel: "ai"
tags: ["DiT","分数匹配","扩散模型","数值稳定性","欧拉-丸山"]
---

# 前向扩散得分精度不能保证扩散采样的数值稳定性

## AI 点评

> 这篇论文切中要害：扩散模型采样看似稳定，但理论漏洞可能让生成结果突然「爆炸」。对于部署扩散模型到生产环境的工程师，这是必读警告。论文不仅指出问题，还给出了投影去噪器这一实用解决方案，值得所有生成模型开发者关注。

## 速览

本文证明，扩散模型中前向扩散的得分匹配误差小并不能保证反向离散化采样数值稳定。作者构造了光滑得分场，其前向边际L²误差、路径空间总变差距离均任意小，但欧拉-丸山离散化后Wasserstein距离发散。对于紧支撑数据，将去噪器投影到已知有界闭凸集可恢复稳定性。实验用小DiT网络验证了稀有轨迹上的数值爆炸及投影抑制效果。

## 关键点

- 前向扩散得分匹配误差小不足以保障反向采样数值稳定，存在反例使Wasserstein距离发散
- 构造的反例中得分场光滑，且反向过程在连续时间上正确，但欧拉-丸山离散化导致矩发散
- 对于紧支撑数据，将去噪器投影到支撑的凸包可同时保持精度并得到均匀矩界
- 小DiT网络实验显示稀有轨迹出现数值爆炸，投影机制有效抑制

## 全文

Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory. We show that small forward-marginal error does not guarantee numerical stability. We construct a single smooth score field with arbitrarily small forward-marginal $L^2$ error. The learned reverse-time process is nonexplosive, has moments of every order, and can be arbitrarily close to the exact reverse-time process in path-space total variation. Yet its Euler--Maruyama discretizations converge in probability while every positive moment diverges. Thus weak convergence can hold even though every Wasserstein distance $W_p$, $p\ge1$, diverges. The same failure can occur within one fixed finite neural architecture. We construct a family of bounded, globally Lipschitz denoisers for which both the forward-marginal error and the path-space total variation distance tend to zero, while their Euler--Maruyama endpoints diverge in every $W_p$. For compactly supported data, we also give a simple positive result. Projecting the learned denoiser onto a known bounded closed convex set containing the support preserves pointwise accuracy, gives grid-uniform moment bounds, and yields Wasserstein convergence under mild local regularity. Experiments with a small fixed DiT-style network show large growth along rare numerical trajectories and its suppression by denoiser projection, while overall trajectory errors remain small.

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引用前请核对原文;本文由星际流动整理:https://feed.astralor.com/items/itm_b9050a5597b829187d93e38a