# Source Separation by Flow Matching

arXiv: https://arxiv.org/abs/2505.16119 · HTML: https://mlsanity.com/paper/2505.16119/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 38 of its 45 references that are in the map.
- First posted on arXiv 22 May 2025.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 30 of 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Deep clustering: Discriminative embeddings for segmentation and separation](https://mlsanity.com/paper/1508.04306/) (2015)
- [DNSMOS P.835: A Non-Intrusive Perceptual Objective Speech Quality Metric to Evaluate Noise Suppressors](https://mlsanity.com/paper/2110.01763/) (2021)
- [Looking to Listen at the Cocktail Party: A Speaker-Independent Audio-Visual Model for Speech Separation](https://mlsanity.com/paper/1804.03619/) (2018)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Let us Build Bridges: Understanding and Extending Diffusion Generative Models](https://mlsanity.com/paper/2208.14699/) (2022)
- [Multi-talker Speech Separation with Utterance-level Permutation Invariant Training of Deep Recurrent Neural Networks](https://mlsanity.com/paper/1703.06284/) (2017)
- [PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior](https://mlsanity.com/paper/2106.06406/) (2021)
- [Non-Denoising Forward-Time Diffusions](https://mlsanity.com/paper/2312.14589/) (2023)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [Diffusion-based Generative Speech Source Separation](https://mlsanity.com/paper/2210.17327/) (2022)
- [SpecGrad: Diffusion Probabilistic Model based Neural Vocoder with Adaptive Noise Spectral Shaping](https://mlsanity.com/paper/2203.16749/) (2022)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)
- [Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching](https://mlsanity.com/paper/2403.18705/) (2024)
- [Diffusion Models for Audio Restoration](https://mlsanity.com/paper/2402.09821/) (2024)

## Built on by (most cited first, 8 of 8)

- [StrADiff: A Structured Source-Wise Adaptive Diffusion Framework for Linear and Nonlinear Blind Source Separation](https://mlsanity.com/paper/2604.04973/) (2026)
- [Geneses: Unified Generative Speech Enhancement and Separation](https://mlsanity.com/paper/2601.18456/) (2026)
- [Conditional Flow Matching for Visually-Guided Acoustic Highlighting](https://mlsanity.com/paper/2602.03762/) (2026)
- [SequenceLayers: Sequence Processing and Streaming Neural Networks Made Easy](https://mlsanity.com/paper/2507.23292/) (2025)
- [Predictive-Generative Drift Decomposition for Speech Enhancement and Separation](https://mlsanity.com/paper/2605.06189/) (2026)
- [SURF: Separation via Unsupervised Remixing Flow](https://mlsanity.com/paper/2606.04921/) (2026)
- [MeCo: One-Step MeanFlow-based Corrector for Multi-Channel Speech Separation](https://mlsanity.com/paper/2606.09677/) (2026)
- [Iterative Audio Separation with Mixture Consistency via MIMO Model Extension](https://mlsanity.com/paper/2609.07226/) (2026)

## Abstract (arXiv)

We consider the problem of single-channel audio source separation with the goal of reconstructing K sources from their mixture. We address this ill-posed problem with FLOSS (FLOw matching for Source Separation), a constrained generation method based on flow matching, ensuring strict mixture consistency. Flow matching is a general methodology that, when given samples from two probability distributions defined on the same space, learns an ordinary differential equation to output a sample from one of the distributions when provided with a sample from the other. In our context, we have access to samples from the joint distribution of K sources and so the corresponding samples from the lower-dimensional distribution of their mixture. To apply flow matching, we augment these mixture samples with artificial noise components to match the dimensionality of the K source distribution. Additionally, as any permutation of the sources yields the same mixture, we adopt an equivariant formulation of flow matching which relies on a neural network architecture that is equivariant by design. We demonstrate the performance of the method for the separation of overlapping speech.