# AR-Flow VAE: A Structured Autoregressive Flow Prior Variational Autoencoder for Unsupervised Blind Source Separation

arXiv: https://arxiv.org/abs/2603.14441 · HTML: https://mlsanity.com/paper/2603.14441/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 22 of 22)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Variational Autoencoder with Learned Latent Structure](https://mlsanity.com/paper/2006.10597/) (2020)
- [Conditional Flow Variational Autoencoders for Structured Sequence Prediction](https://mlsanity.com/paper/1908.09008/) (2019)
- [Scalable Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.13472/) (2020)
- [Markovian Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2207.05543/) (2022)
- [Revisiting Structured Variational Autoencoders](https://mlsanity.com/paper/2305.16543/) (2023)
- [Half-AVAE: Adversarial-Enhanced Factorized and Structured Encoder-Free VAE for Underdetermined Independent Component Analysis](https://mlsanity.com/paper/2506.07011/) (2025)
- [Structured Kernel Regression VAE: A Computationally Efficient Surrogate for GP-VAEs in ICA](https://mlsanity.com/paper/2508.09721/) (2025)
- [Identifiable Autoregressive Variational Autoencoders for Nonlinear and Nonstationary Spatio-Temporal Blind Source Separation](https://mlsanity.com/paper/2509.11962/) (2025)

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

- [PDGMM-VAE: A Variational Autoencoder with Adaptive Per-Dimension Gaussian Mixture Model Priors for Nonlinear ICA](https://mlsanity.com/paper/2603.23547/) (2026)
- [SAHMM-VAE: A Source-Wise Adaptive Hidden Markov Prior Variational Autoencoder for Unsupervised Blind Source Separation](https://mlsanity.com/paper/2603.25776/) (2026)

## Abstract (arXiv)

Blind source separation (BSS) seeks to recover latent source signals from observed mixtures. Variational autoencoders (VAEs) offer a natural perspective for this problem: the latent variables can be interpreted as source components, the encoder can be viewed as a demixing mapping from observations to sources, and the decoder can be regarded as a remixing process from inferred sources back to observations. In this work, we propose AR-Flow VAE, a novel VAE-based framework for BSS in which each latent source is endowed with a parameter-adaptive autoregressive flow prior. This prior significantly enhances the flexibility of latent source modeling, enabling the framework to capture complex non-Gaussian behaviors and structured dependencies, such as temporal correlations, that are difficult to represent with conventional priors. In addition, the structured prior design assigns distinct priors to different latent dimensions, thereby encouraging the latent components to separate into different source signals under heterogeneous prior constraints. Experimental results validate the effectiveness of the proposed architecture for blind source separation. More importantly, this work provides a foundation for future investigations into the identifiability and interpretability of AR-Flow VAE.