用扩散模型从多视角数据中分离未知源，无需预设源结构。
A Data-Driven Prism: Multi-View Source Separation with Diffusion Model Priors
- 基于多视角观测的线性变换特性，不依赖源的先验假设。
- 在噪声、缺失与分辨率差异下仍能成功分离，支持概率采样与后验推断。
- 适用于天体、神经信号等复杂源分离任务，尤其适合无标签数据场景。
自然科学研究中常见难题是将未知的多个源从观测数据中解耦。例如，在密集星场中分离星系、从重叠信号中区分单个神经元活动，或从背景噪声中分离地震事件。传统方法常依赖简化的源模型，难以准确还原真实数据。近期研究显示，扩散模型可直接从噪声和不完整数据中学习复杂先验分布。本文提出一种新方法，仅利用多视角观测——即不同观测集合包含未知源的不同线性变换——即可实现源分离，无需对源结构做显式假设。该方法在无任何源被单独观测、且数据存在噪声、缺失与分辨率差异时仍表现有效。所学扩散模型可用于从源先验中采样、评估候选源的概率，并推断给定观测下的源联合后验分布。我们在一系列合成问题及真实星系观测中验证了该方法的有效性。
原文摘要 · Abstract (English)
A common challenge in the natural sciences is to disentangle distinct, unknown sources from observations. Examples of this source separation task include deblending galaxies in a crowded field, distinguishing the activity of individual neurons from overlapping signals, and separating seismic events from an ambient background. Traditional analyses often rely on simplified source models that fail to accurately reproduce the data. Recent advances have shown that diffusion models can directly learn complex prior distributions from noisy, incomplete data. In this work, we show that diffusion models can solve the source separation problem without explicit assumptions about the source. Our method relies only on multiple views, or the property that different sets of observations contain different linear transformations of the unknown sources. We show that our method succeeds even when no source is individually observed and the observations are noisy, incomplete, and vary in resolution. The learned diffusion models enable us to sample from the source priors, evaluate the probability of candidate sources, and draw from the joint posterior of the source distribution given an observation. We demonstrate the effectiveness of our method on a range of synthetic problems as well as real-world galaxy observations.
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