MeCo: One-Step MeanFlow-based Corrector for Multi-Channel Speech Separation

Abstract: While discriminative models for multi-channel speech separation excel in reference-based metrics, they often exhibit suboptimal human listening quality. To address this, we propose a novel MeanFlow-based one-step generative corrector (MeCo). MeCo learns a conditional average velocity field to map discriminative estimates directly onto the clean speech manifold in a single step. To maximize one-step generation performance, we introduce Data-Space Optimization (DSO). DSO integrates an $\mathbf{x}_r$-loss, which penalizes prediction errors on longer displacement intervals to serve as a generative objective for human listening quality, with an Endpoint SI-SDR loss that directly optimizes terminal signal fidelity. Experiments demonstrate that MeCo achieves state-of-the-art (SOTA) performance with minimal computational overhead, simultaneously achieving superior signal fidelity and human listening quality in both in-domain and out-of-domain scenarios.

• The paper introduces MeCo, a one-step MeanFlow-based corrector that deterministically maps separator output to the clean speech manifold in a single operation.
• It integrates data-space optimization with combined x_r-loss and endpoint SI-SDR losses, resulting in superior SI-SDR and perceptual quality metrics.
• Experiments demonstrate MeCo’s robustness across multi-channel mixtures, improved deployment efficiency, and potential for real-time applications.

One-Step MeanFlow-Based Correction for Multi-Channel Speech Separation

Problem Overview and Motivation

The paper addresses the inherent trade-off in multi-channel speech separation systems between reference-based objective signal fidelity and the subjective perceptual quality experienced by human listeners. Discriminative models, while achieving high SI-SDR and related metrics, often inject perceptual artifacts that degrade listener experience as captured by DNSMOS, UTMOS, and related perceptual metrics. In contrast, generative models, especially those based on diffusion and flow architectures, better preserve naturalness but suffer from high inference latency due to iterative sampling and are rarely practical for real-world deployment in multi-channel settings.

Prior work attempts to bridge these paradigms via cascaded approaches—first applying a discriminative separator, followed by a generative model as a corrector. Notably, one-step correctors like Fast-GeCo reduce inference cost, but their reliance on SI-SNR-only objectives and heuristic trajectory truncation introduce prior mismatches and limit perceptual quality. Additionally, Fast-GeCo's two-stage training complicates practical application. No fully end-to-end, one-step generative corrector has been extended efficiently to multi-channel scenarios prior to this work.

MeCo Architecture and Methodology

The proposed system, MeCo, leverages the MeanFlow framework for one-step generative correction. MeanFlow differs fundamentally from classical Flow Matching by predicting the average velocity field over a global trajectory segment, rather than the instantaneous field. This allows MeCo to deterministically map the discriminative separator’s output directly onto the clean speech manifold in a single operation, elegantly eliminating the previously-noted distribution mismatch.

The system operates in the STFT domain, conditioning both on the multi-channel mixture and the separator's output. For each target speaker, MeCo learns a conditional Gaussian path from the distorted estimate to the clean reference with analytically scheduled mean and variance. The network is explicitly conditioned on spatial mixture information and uses the first-order MeanFlow identity for training, stabilized with a correction factor and stop-gradient regularization for higher-order derivatives.

Data-Space Optimization Training Paradigm

To maximize both signal fidelity and perceptual quality, MeCo augments MeanFlow training with Data-Space Optimization (DSO):

• $\mathbf{x}_r$-loss: This novel objective penalizes the predicted versus target data point deviation at arbitrary integration intervals, inherently weighting long displacements more heavily—crucial for one-step inference where $\Delta \approx 1$. This shifts the training regime towards reconstructing natural clean speech structure in a single generative step.
• Endpoint SI-SDR loss: In parallel, the system minimizes negative SI-SDR directly between the one-step output and the clean target, ensuring high terminal signal fidelity beyond Euclidean reconstruction error minimization.
• Combined loss: By summing these objectives, MeCo optimally aligns the velocity field for both deterministic and generative quality criteria.

This direct data-space alignment is a central innovation, yielding strong perceptual gains without sacrificing metric performance.

Experimental Results and Analysis

MeCo was evaluated against strong baselines (e.g., DeFTAN2, SpatialNet, CrossNet), standalone generative correctors (Fast-GeCo, MeanFlow), and in both in-domain (WSJ0+WHAM!) and out-of-domain (Librispeech+DEMAND, low-resource languages) conditions. All correctors introduced just one additional function evaluation and negligible runtime overhead.

Key findings include:

• Superior SI-SDR and perceptual quality: MeCo consistently exceeds or matches baselines on SI-SDR and PESQ, and offers substantial improvements on DNSMOS, UTMOS, and NISQA metrics.
• Generality and robustness: MeCo outperforms both discriminative and existing generative correctors on entirely unseen language and noise conditions, driven by its generative DSO framework rather than SI-SDR-only training.
• Ablation evidence: Including both $\mathbf{x}_r$-loss and endpoint SI-SDR loss yields optimal performance, with incremental gains from each component individually.

These results highlight the claim that one-step mean flow-based generative correction combining data- and signal-space losses can achieve state-of-the-art objective and perceptual quality with minimal latency in multi-channel speech separation.

Theoretical and Practical Implications

From a theoretical perspective, the extension of MeanFlow average velocity fields to conditional, multi-channel scenarios is non-trivial. The empirical demonstration that one-step DSO-trained models can outperform iterative correctors—while maintaining speed—points towards more generalizable and scalable generative refinement for structured data. The explicit penalization of displacement via $\Delta^2$-scaling is especially significant for the effective training of one-step correctors.

Practically, the architecture is highly deployable. By avoiding multi-stage training, eliminating iterative refinement, and supporting arbitrary multi-channel mixtures, MeCo offers a route to real-time, high-fidelity, human-pleasing source separation in real-world devices, communication systems, or hearing aids.

Future Research

The current MeCo implementation relies on independent channel-wise concatenation for speaker refinement and does not model explicit inter-speaker dependencies. Future work may incorporate spatial beamforming, joint multi-speaker correction, and more sophisticated joint spatial-spectral modeling. Extensions to more complex acoustic scenes, variable microphone layouts, and low-compute edge environments are promising directions. Additionally, adaptation of the DSO paradigm to other domains (e.g., music separation, enhancement in reverberant environments) would be a natural progression.

Conclusion

The MeCo framework introduces a mathematically principled, computationally efficient, and highly effective approach for one-step generative correction in multi-channel speech separation (2606.09677). By leveraging MeanFlow and DSO, it unifies the strengths of discriminative and generative methods, delivering high performance on both traditional and perceptual speech quality metrics with practical deployment characteristics. This work establishes a robust foundation for future scalable generative refiners in speech processing.