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

arXiv: https://arxiv.org/abs/2604.04973 · HTML: https://mlsanity.com/paper/2604.04973/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 27 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Denoising Diffusion Autoencoders are Unified Self-supervised Learners](https://mlsanity.com/paper/2303.09769/) (2023)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [SODA: Bottleneck Diffusion Models for Representation Learning](https://mlsanity.com/paper/2311.17901/) (2023)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)
- [DisDiff: Unsupervised Disentanglement of Diffusion Probabilistic Models](https://mlsanity.com/paper/2301.13721/) (2023)
- [Diffusion Model with Cross Attention as an Inductive Bias for Disentanglement](https://mlsanity.com/paper/2402.09712/) (2024)
- [Score-based Source Separation with Applications to Digital Communication Signals](https://mlsanity.com/paper/2306.14411/) (2023)
- [Source Separation by Flow Matching](https://mlsanity.com/paper/2505.16119/) (2025)
- [ArrayDPS: Unsupervised Blind Speech Separation with a Diffusion Prior](https://mlsanity.com/paper/2505.05657/) (2025)
- [Disentangling Disentangled Representations: Towards Improved Latent Units via Diffusion Models](https://mlsanity.com/paper/2410.23820/) (2024)
- [PDGMM-VAE: A Variational Autoencoder with Adaptive Per-Dimension Gaussian Mixture Model Priors for Nonlinear ICA](https://mlsanity.com/paper/2603.23547/) (2026)
- [Can Diffusion Models Disentangle? A Theoretical Perspective](https://mlsanity.com/paper/2504.00220/) (2025)
- [A Data-Driven Prism: Multi-View Source Separation with Diffusion Model Priors](https://mlsanity.com/paper/2510.05205/) (2025)

## Built on by (most cited first, 2 of 2)

- [StrEBM: A Structured Latent Energy-Based Model for Blind Source Separation](https://mlsanity.com/paper/2604.17381/) (2026)
- [StrTransformer: Source-Wise Structured Transformers for Unsupervised Blind Source Recovery](https://mlsanity.com/paper/2605.25648/) (2026)

## Abstract (arXiv)

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.