StrADiff: A Structured Source-Wise Adaptive Diffusion Framework for Linear and Nonlinear Blind Source Separation

2026-04-04

AI Summary

This work addresses the lack of structured modeling of source components in both linear and nonlinear blind source separation by proposing a structured, source-adaptive diffusion framework. The method treats each latent dimension as an independent source signal, equipping it with a dedicated adaptive diffusion mechanism and incorporating source-specific Gaussian process priors to capture temporal structure. Through end-to-end joint optimization, the framework unifies the treatment of linear and nonlinear mixing scenarios, enabling unsupervised recovery of source signals, disentanglement of components, and learning of identifiable latent representations. To the best of our knowledge, this is the first approach to implement adaptive diffusion modeling at the level of individual source components, offering both interpretability and extensibility while remaining compatible with other structured priors.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Bridging structured and unstructured data

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.

Problem

• blind source separation
• structured latent modeling
• nonlinear mixing
• source-wise disentanglement
• unsupervised source recovery

Innovation

• structured diffusion
• source-wise adaptation
• blind source separation
• adaptive Gaussian process prior
• latent disentanglement