# Training-Free Multi-Step Audio Source Separation

arXiv: https://arxiv.org/abs/2505.19534 · HTML: https://mlsanity.com/paper/2505.19534/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 58 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 30 of 48)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [UTMOS: UTokyo-SaruLab System for VoiceMOS Challenge 2022](https://mlsanity.com/paper/2204.02152/) (2022)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [DNSMOS: A Non-Intrusive Perceptual Objective Speech Quality metric to evaluate Noise Suppressors](https://mlsanity.com/paper/2010.15258/) (2020)
- [Inference-Time Scaling for Diffusion Models beyond Scaling Denoising Steps](https://mlsanity.com/paper/2501.09732/) (2025)
- [Speech Enhancement and Dereverberation with Diffusion-based Generative Models](https://mlsanity.com/paper/2208.05830/) (2022)
- [Attention is All You Need in Speech Separation](https://mlsanity.com/paper/2010.13154/) (2020)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [The INTERSPEECH 2020 Deep Noise Suppression Challenge: Datasets, Subjective Testing Framework, and Challenge Results](https://mlsanity.com/paper/2005.13981/) (2020)
- [Wave-U-Net: A Multi-Scale Neural Network for End-to-End Audio Source Separation](https://mlsanity.com/paper/1806.03185/) (2018)
- [Music Source Separation in the Waveform Domain](https://mlsanity.com/paper/1911.13254/) (2019)
- [Music Source Separation with Band-split RNN](https://mlsanity.com/paper/2209.15174/) (2022)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [WHAMR!: Noisy and Reverberant Single-Channel Speech Separation](https://mlsanity.com/paper/1910.10279/) (2019)
- [TorchAudio-Squim: Reference-less Speech Quality and Intelligibility measures in TorchAudio](https://mlsanity.com/paper/2304.01448/) (2023)
- [A scalable noisy speech dataset and online subjective test framework](https://mlsanity.com/paper/1909.08050/) (2019)
- [Decoupling Magnitude and Phase Estimation with Deep ResUNet for Music Source Separation](https://mlsanity.com/paper/2109.05418/) (2021)

## Built on by (most cited first, 1 of 1)

- [Iterative Audio Separation with Mixture Consistency via MIMO Model Extension](https://mlsanity.com/paper/2609.07226/) (2026)

## Abstract (arXiv)

Audio source separation aims to separate a mixture into target sources. Previous audio source separation systems usually conduct one-step inference, which does not fully explore the separation ability of models. In this work, we reveal that pretrained one-step audio source separation models can be leveraged for multi-step separation without additional training. We propose a simple yet effective inference method that iteratively applies separation by optimally blending the input mixture with the previous step's separation result. At each step, we determine the optimal blending ratio by maximizing a metric. We prove that our method always yield improvement over one-step inference, provide error bounds based on model smoothness and metric robustness, and provide theoretical analysis connecting our method to denoising along linear interpolation paths between noise and clean distributions, a property we link to denoising diffusion bridge models. Our approach effectively delivers improved separation performance as a "free lunch" from existing models. Our empirical results demonstrate that our multi-step separation approach consistently outperforms one-step inference across both speech enhancement and music source separation tasks, and can achieve scaling performance similar to training a larger model, using more data, or in some cases employing a multi-step training objective. These improvements appear not only on the optimization metric during multi-step inference, but also extend to nearly all non-optimized metrics (with one exception). We also discuss limitations of our approach and directions for future research.