提出一种无需标签的盲源分离框架,可直接从混合信号中恢复潜在源轨迹。
StrADiff: A Structured Source-Wise Adaptive Diffusion Framework for Linear and Nonlinear Blind Source Separation

- 为每个潜在维度设计自适应反向扩散机制,实现端到端源分离。
- 在线性混合下表现稳定,非线性混合下性能略有下降。
- 适用于信号分离与可解释性表征学习,适合对结构化潜空间建模的研究者。
本文提出StrADiff,一种面向线性和非线性混合的无监督盲源分离结构化源级自适应扩散框架。该框架将每个隐变量维度视为一个源分支,并为其分配独立的自适应反向扩散机制,使潜在源能通过单一端到端目标直接从观测混合中恢复,无需监督源标签或后续处理。源级生成、结构正则化和观测空间重建在训练中联合优化。本实例采用高斯过程(GP)先验作为源级结构先验,以对恢复轨迹施加时间组织约束;框架本身不限于GP先验,原则上可融入其他结构先验。理论部分阐明了诱导的前推源分布、结构先验在样本层面的作用、源恢复与先验自适应间的耦合关系,以及理想线性低噪声情形下的条件弱恢复结论。在线性和非线性混合实验中,StrADiff均能无监督地恢复有意义的潜在源轨迹,线性情况下表现稳定,非线性下性能适度下降。除经典信号分离外,源分支亦可在适当结构假设下被解释为独立、解耦或可解释的解释因子,暗示了一条通往结构化潜空间建模与未来可识别非线性表征学习的新路径。
原文摘要 · Abstract (English)
This paper presents StrADiff, a Structured Source-Wise Adaptive Diffusion Framework for unsupervised blind source separation under linear and nonlinear mixing. The framework treats each latent dimension as a source branch and assigns to it an individual adaptive reverse diffusion mechanism, so that latent sources are recovered directly from observed mixtures through a single end-to-end objective, without supervised source labels or separate post-processing. Source-wise generation, structural regularization, and observation-space reconstruction are optimized jointly during training. In this instantiation, a Gaussian process (GP) prior is used as one example of a source-wise structured prior to impose temporal organization on each recovered trajectory; the framework itself is not restricted to GP priors and can in principle incorporate other structured priors. Theoretical components clarify the induced pushforward source law, the sample-level role of the structured prior, the coupling between source recovery and prior adaptation, and a conditional weak recovery statement in an idealized linear low-noise regime. Experiments on linear and nonlinear mixtures show that StrADiff can recover meaningful latent source trajectories in an unsupervised manner, with particularly stable performance in the linear case and moderate degradation under nonlinear mixing. Beyond classical signal separation, a source branch may also be interpreted as an independent, disentangled, or otherwise interpretable explanatory factor under suitable structural assumptions, suggesting a broader route toward structured latent modeling and future identifiable nonlinear representation learning.
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