# Discriminative Flow Matching: Beyond Time-Conditioning in Generative Restoration via Flow-State Representations

arXiv: https://arxiv.org/abs/2609.04525 · HTML: https://mlsanity.com/paper/2609.04525/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
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- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [DNSMOS: A Non-Intrusive Perceptual Objective Speech Quality metric to evaluate Noise Suppressors](https://mlsanity.com/paper/2010.15258/) (2020)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [DCCRN: Deep Complex Convolution Recurrent Network for Phase-Aware Speech Enhancement](https://mlsanity.com/paper/2008.00264/) (2020)
- [The INTERSPEECH 2020 Deep Noise Suppression Challenge: Datasets, Subjective Testing Framework, and Challenge Results](https://mlsanity.com/paper/2005.13981/) (2020)
- [Conditional Diffusion Probabilistic Model for Speech Enhancement](https://mlsanity.com/paper/2202.05256/) (2022)
- [MetricGAN+: An Improved Version of MetricGAN for Speech Enhancement](https://mlsanity.com/paper/2104.03538/) (2021)
- [StoRM: A Diffusion-based Stochastic Regeneration Model for Speech Enhancement and Dereverberation](https://mlsanity.com/paper/2212.11851/) (2022)
- [Speech Enhancement with Score-Based Generative Models in the Complex STFT Domain](https://mlsanity.com/paper/2203.17004/) (2022)
- [A Recurrent Variational Autoencoder for Speech Enhancement](https://mlsanity.com/paper/1910.10942/) (2019)
- [SCOREQ: Speech Quality Assessment with Contrastive Regression](https://mlsanity.com/paper/2410.06675/) (2024)
- [FlowAVSE: Efficient Audio-Visual Speech Enhancement with Conditional Flow Matching](https://mlsanity.com/paper/2406.09286/) (2024)
- [Diffusion-based Generative Modeling with Discriminative Guidance for Streamable Speech Enhancement](https://mlsanity.com/paper/2406.13471/) (2024)
- [Deep Noise Suppression Maximizing Non-Differentiable PESQ Mediated by a Non-Intrusive PESQNet](https://mlsanity.com/paper/2111.03847/) (2021)
- [SE-Bridge: Speech Enhancement with Consistent Brownian Bridge](https://mlsanity.com/paper/2305.13796/) (2023)
- [Ultra Low Complexity Deep Learning Based Noise Suppression](https://mlsanity.com/paper/2312.08132/) (2023)
- [GAN-Based Speech Enhancement for Low SNR Using Latent Feature Conditioning](https://mlsanity.com/paper/2410.13599/) (2024)
- [Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement](https://mlsanity.com/paper/2508.20584/) (2025)
- [Generative Control as Optimization: Time Unconditional Flow Matching for Adaptive and Robust Robotic Control](https://mlsanity.com/paper/2603.17834/) (2026)
- [GALD-SE: Guided Anisotropic Lightweight Diffusion for Efficient Speech Enhancement](https://mlsanity.com/paper/2409.15101/) (2024)
- [Time-Unconditional Generative Speech Enhancement via Autonomous Rectified Flow](https://mlsanity.com/paper/2606.20001/) (2026)

## Abstract (arXiv)

Existing Conditional Flow Matching (CFM) formulations describe transport progress using an explicit interpolation coordinate, commonly interpreted as time, assuming that a single global variable adequately represents a sample's position along the generative trajectory. In restoration tasks, however, transport progress is sample-dependent because the initial distribution may exhibit varying statistical dependencies with the target distribution. Thus, samples at the same interpolation coordinate can differ substantially in degradation level, distance to the target distribution, and restoration difficulty. We investigate whether signal representations learned by discriminatively trained models provide a meaningful description of generative transport state in CFM-based restoration. Through systematic latent-space analysis, we show that discriminative representations organize according to degradation severity and follow a consistent trajectory toward the clean-data manifold during generation. Motivated by these observations, we introduce the Discriminative Flow-State Hypothesis, which posits that discriminative representations encode a transport state governing generative restoration. Based on this hypothesis, we propose Discriminative Flow Matching, which conditions the Flow-Matching velocity field on Discriminative Flow-State Representations rather than explicit time coordinates. Experiments on speech enhancement and image denoising show that these representations characterize restoration progress, enable adaptive inference, and consistently outperform CFM and diffusion-related baselines. Our findings suggest that discriminative representations provide an effective state-aware alternative to explicit time conditioning and offer a novel perspective on the relationship between discriminative and CFM-based generative modeling.