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.

翻译：本文提出StrADiff——一种用于线性与非线性混合下无监督盲源分离的结构化源适应扩散框架。该框架将每个潜在维度视为一个源分支，并为其分配独立的适应反向扩散机制，从而通过单一端到端目标直接从观测混合数据中恢复潜在源，无需监督源标签或单独的后处理。训练过程中联合优化源分支生成、结构化正则化与观测空间重建。在本实例中，采用高斯过程先验作为源分支结构化先验的示例，以对每条恢复轨迹施加时间序结构；但框架本身不限于高斯过程先验，原则上可整合其他结构化先验。理论分析阐明了诱导前推源分布、结构化先验的样本级作用、源恢复与先验适应之间的耦合关系，以及在理想线性低噪声条件下的条件弱恢复性结论。在线性与非线性混合实验表明，StrADiff能够以无监督方式恢复有意义的潜在源轨迹，在线性混合中性能尤为稳定，而非线性混合下性能适度衰减。超越经典信号分离范畴，在适当结构假设下，源分支可被解读为独立、解缠或具可解释性的解释性因子，这为结构化潜在建模及未来可辨识非线性表示学习开辟了更广阔路径。