Ambient diffusion is a recently proposed framework for training diffusion
models using corrupted data. Both Ambient Diffusion and alternative SURE-based
approaches for learning diffusion models from corrupted data resort to
approximations which deteriorate performance. We present the first framework
for training diffusion models that provably sample from the uncorrupted
distribution given only noisy training data, solving an open problem in this
space. Our key technical contribution is a method that uses a double
application of Tweedie's formula and a consistency loss function that allows us
to extend sampling at noise levels below the observed data noise. We also
provide further evidence that diffusion models memorize from their training
sets by identifying extremely corrupted images that are almost perfectly
reconstructed, raising copyright and privacy concerns. Our method for training
using corrupted samples can be used to mitigate this problem. We demonstrate
this by fine-tuning Stable Diffusion XL to generate samples from a distribution
using only noisy samples. Our framework reduces the amount of memorization of
the fine-tuning dataset, while maintaining competitive performance.

我们提出了第一个从嘈杂的训练数据中获得未污染分布样本的扩散模型训练框架，使用了 Tweedie 公式的双重应用和一致性损失函数。我们还通过识别几乎完美重建的极度受损图像来提供扩散模型记忆训练集的进一步证据，引发了版权和隐私问题。我们的训练方法可用于缓解这个问题，并展示了通过对 Stable Diffusion XL 进行微调，使用仅嘈杂样本生成分布样本的能力。我们的框架减少了微调数据集的记忆量，同时保持有竞争力的性能。

一致扩散遇到 Tweedie：用有噪数据训练准确的环境扩散模型

Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion  Models with Noisy Data

In this paper, we focus on weakly supervised learning with noisy training
data for both classification and regression problems.We assume that the
training outputs are collected from a mixture of a target and correlated noise
distributions.Our proposed method simultaneously estimates the target
distribution and the quality of each data which is defined as the correlation
between the target and data generating distributions.The cornerstone of the
proposed method is a Cholesky Block that enables modeling dependencies among
mixture distributions in a differentiable manner where we maintain the
distribution over the network weights.We first provide illustrative examples in
both regression and classification tasks to show the effectiveness of the
proposed method.Then, the proposed method is extensively evaluated in a number
of experiments where we show that it constantly shows comparable or superior
performances compared to existing baseline methods in the handling of noisy
data.

本文研究了一种基于 Cholesky Block 的方法，该方法能够同时估计数据的质量和目标分布，并有效地处理带有噪声的弱监督学习问题，包括分类和回归。实验证明，该方法在处理噪声数据方面表现出与基准方法相当或更好的性能。

基于相关性引导混合密度网络的失真输出下任务无关鲁棒学习

Task Agnostic Robust Learning on Corrupt Outputs by Correlation-Guided  Mixture Density Networks

Score matching is a recently developed parameter learning method that is
particularly effective to complicated high dimensional density models with
intractable partition functions. In this paper, we study two issues that have
not been completely resolved for score matching. First, we provide a formal
link between maximum likelihood and score matching. Our analysis shows that
score matching finds model parameters that are more robust with noisy training
data. Second, we develop a generalization of score matching. Based on this
generalization, we further demonstrate an extension of score matching to models
of discrete data.

本文研究了评分匹配在解决高维密度模型中不可处理的分区函数时所用到的两个问题：首先，提供了最大似然和评分匹配之间的正式联系，其分析表明评分匹配可以找到更具有噪音训练数据鲁棒性的模型参数；其次，本文还发展了评分匹配的一个推广，并在此基础上进一步展示了将其扩展到离散数据模型的方法。