Abstract
This paper presents a Structured Source-Wise Adaptive Diffusion Framework for linear and nonlinear blind source separation. The framework interprets each latent dimension as a source component and assigns to it an individual adaptive diffusion mechanism, thereby establishing source-wise latent modeling rather than relying on a single shared latent prior. The resulting formulation learns source recovery and the mixing/reconstruction process jointly within a unified end-to-end objective, allowing model parameters and latent sources to adapt simultaneously during training. This yields a common framework for both linear and nonlinear blind source separation. In the present instantiation, each source is further equipped with its own adaptive Gaussian process (GP) prior to impose source-wise temporal structure on the latent trajectories, while the overall framework is not restricted to Gaussian process priors and can in principle accommodate other structured source priors. The proposed model thus provides a general structured diffusion-based route to unsupervised source recovery, with potential relevance beyond blind source separation to interpretable latent modeling, source-wise disentanglement, and potentially identifiable nonlinear latent-variable learning under appropriate structural conditions.
Abstract (translated)
本文提出了一种用于线性和非线性盲源分离的结构化按源自适应扩散框架。该框架将每个潜在维度解释为一个源分量，并为其分配独立的自适应扩散机制，从而建立了按源潜在建模，而非依赖单一共享的潜在先验。由此产生的公式在统一的端到端目标函数中联合学习源恢复与混合/重建过程，使模型参数和潜在源在训练过程中同步自适应。这为线性和非线性盲源分离提供了一个通用框架。在当前的实现中，每个源还配备了各自的自适应高斯过程（GP）先验，以对潜在轨迹施加按源的时间结构约束，而整体框架不限于高斯过程先验，原则上可容纳其他结构化源先验。因此，所提出的模型提供了一种通用的基于结构化扩散的无监督源恢复路径，在适当结构条件下，其潜在意义不仅限于盲源分离，还可拓展至可解释的潜在建模、按源解耦以及可能可识别的非线性潜在变量学习。
URL
https://arxiv.org/abs/2604.04973
