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.
Figures & tables
Figure 1: Comparison of conditioning strategies for Flow-based restoration tasks. (a) CFM conditions the velocity field on t . (b) Autonomous Rectified Flow (ARF) removes t . (c) CFM+DL conditions CFM with the additional discriminative latent (DL) representation zt=Eϕ(xt) . (d) DFM replaces t with the Discriminative Flow-State Representation z=Eϕ(xζ).
Figure 2: t-SNE visualization of DCCRN latent representations under (a) rain and (b) machinery noise.
Figure 3: Prediction of observable Flow-State quantities from either the DFSR or the anchor-based signal pair.
Target
Method
MAE ↓
RMSE ↓
Pearson ↑
iSNR
Latent
0.032
0.047
0.968
Anchor
0.035
0.048
0.971
gSNR
Latent
0.117
0.154
0.491
Anchor
0.142
0.181
0.301
ζ
Latent
0.154
0.190
0.741
Anchor
0.155
0.211
0.751
Table 1: Prediction performance for quantities related to the Flow-State. Best results are shown in bold .
Figure 4: Evolution of signal-space and latent-space Flow-States over NFE.
Cat.
Method
SI-SDR ( ↑ )
PESQ ( ↑ )
SCOREQ Ref. ( ↓ )
SCOREQ Non-Ref. ( ↑ )
Unproc.
Noisy
9.06
1.58
0.93
2.78
Clean
–
–
0.00
4.60
Disc.
DCCRN
17.36
2.91
0.31
4.15
GCRN
16.71
2.63
0.42
3.87
Diff.
SGMSE+
16.86
2.81
0.29
4.15
BBED
19.10
2.81
0.26
4.38
Table 2: SE results on the DNS Challenge synthetic non-reverberant test set.
Method
P808 MOS ( ↑ )
SIG ( ↑ )
BAK ( ↑ )
OVRL ( ↑ )
Noisy
3.05
3.05
2.51
2.26
RVAE
3.29
3.16
2.91
2.44
CDiffuse
3.14
3.15
3.19
2.55
MetricGAN+
3.26
2.88
3.39
2.45
DisCoGAN
3.65
3.32
3.91
2.98
SGMSE
3.38
3.22
3.02
2.52
Table 3: Generalization results on the DNS Real Recordings test set ( Reddy et al. 2020 ) . Baseline results are taken from their respective original publications.
Method
SI-SDR ( ↑ )
PESQ ( ↑ )
SCOREQ Ref. ( ↓ )
SCOREQ Non-Ref. ( ↑ )
Noisy
9.06
1.58
0.93
2.78
Clean
–
–
0
4.60
CFM
18.74
2.78
0.27
4.32
ARF
18.83
2.79
0.26
4.38
CFM+DL
18.96
2.75
0.26
4.39
DFM (Ours)
19.17
2.88
0.24
4.44
Table 4: Results on the DNS Challenge non-reverberant test set under the data-prediction training objective.
Figure 5: Performance for DFM with adaptive inference.
Figure 6: Complexity-performance trade-off (baselines shown in red, proposed methods in green)
Figure 7: Image denoising performance relative to CFM .
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Figure A8: Relative kNN and MMD distances between noisy latent representations and the clean latent set across different SNR levels. Both measures decrease monotonically with increasing SNR, indicating that intermediate samples progressively approach the clean latent representations.
Metric
Value
Pearson ( r )
−0.9645
Spearman ( ρ )
−0.9832
Monotonicity violations
0/8
Appendix
Table A5: Monotonic relationship between SNR and latent proximity.
Category
Method
Conditioning
SI-SDR ( ↑ )
PESQ ( ↑ )
Unprocessed
Noisy
–
9.06
1.58
Discriminative
DCCRN
NA
17.36
2.91
GCRN
NA
16.71
2.63
TaylorSENet
NA
16.59
2.65
ULCNet
NA
16.70
2.56
CFM
FlowSE
t
18.99
2.86
Appendix
Table A6: DFM results on the DNS Challenge synthetic non-reverberant test set for utilizing discriminative features from different discriminatively trained SE methods.
Input
STFT Match
SI-SDR ( ↑ )
PESQ ( ↑ )
μζ
No
19.48
2.91
μζ
Yes
19.87
2.94
xζ
No
19.74
2.89
xζ
Yes
19.86
2.96
x0
No
19.55
2.92
x0
Yes
19.63
2.96
Appendix
Table A7: Ablation study of DFM on the DNS Challenge synthetic non-reverberant test set where the discriminative model used for conditioning is trained with different inputs and STFT configurations.
Method
SI-SDR ( ↑ )
PESQ ( ↑ )
SCOREQ Ref. ( ↓ )
SCOREQ Non-Ref. ( ↑ )
Noisy
9.06
1.58
0.93
2.78
Clean
–
–
0
4.60
CFM
6.81
1.31
0.76
3.2
ARF
6.86
1.31
0.7
3.35
DFM (Ours)
7.20
1.34
0.67
3.46
Appendix
Table A8: Results on the DNS Challenge non-reverberant test set without using the noisy signal x0 for conditioning the velocity network.
Method
SI-SDR ( ↑ )
PESQ ( ↑ )
SCOREQ Ref. ( ↓ )
SCOREQ Non-Ref. ( ↑ )
Noisy
-31.55
1.32
0.84
2.99
Clean
-
0
4.60
DCCRN
-29.06
1.91
0.87
2.73
CFM
-27.64
2.35
0.59
3.45
DFM (Ours)
-27.19
2.44
0.58
3.47
Appendix
Table A9: Results on the DNS Challenge reverberant test set for a speech dereverberation task.
Figure A9: Architecture of the MNIST and Fashion-MNIST Image Classifier.
Figure A10: Semantic latent structure and latent restoration geometry.
Figure A11: Architecture of the velocity network for image denoising task.
Figure A12: Adaptive inference with uniform Euler solver for image denoising on the MNIST dataset.
Figure A13: PESQ and SI-SDR improvements along with their respective 95% confidence intervals for the compared methods presented in Table 2 .
Baseline Model
PESQ
SI-SDR (dB)
Baseline Mean
p -value
Baseline Mean
p -value
DCCRN
2.91
0.300
17.36
<0.001
GCRN
2.63
<0.001
16.71
<0.001
BBED
2.81
<0.001
19.10
<0.001
SGMSE+
2.81
<0.001
16.86
<0.001
SToRM
2.70
<0.001
17.56
<0.001
Appendix
Table A10: Statistical significance test results (paired Wilcoxon signed-rank test) comparing our proposed DFM method (PESQ: 2.96 , SI-SDR: 19.63 dB ) against various baseline models.
Generative models, particularly diffusion and score-based approaches, have recently achieved strong performance in speech enhancement, but their iterative sampling process limits real-time deployment. Flow Matching offers an efficient alternative by transporting noisy speech toward clean speech through an ordinary differential equation with few function evaluations. In this work, we propose a skip-free encoder-decoder backbone for flow-matching speech enhancement, guided by Latent Representation Alignment (LRA). Instead of relying on U-Net skip connections, which may transfer noise-correlated low-level features to the decoder, the proposed model aligns its bottleneck and decoder representations with clean latent features extracted from a frozen Descript Audio Codec encoder-decoder without quantization. This codec-aligned supervision promotes compact clean-speech representations while preserving efficient few-step inference. Experiments on WSJ0-CHiME3 and VoiceBank-DEMAND show improved PESQ and perceptual quality, especially on VoiceBank-DEMAND, using only five function evaluations.
Wangyi Pu, Michele Scarpiniti
Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Italy
Distilling semantic meaning from raw image data remains a challenge in machine learning. Current self-supervised paradigms face a trade-off: joint-embedding architectures produce relevant features by aggressively discarding intra-class variance, irreversibly spatial and reconstruction. Conversely, generative models preserve spatial details but struggle to isolate semantics, as their optimization is dominated by pixel variations. To bridge this divide, we propose composite subspace flow matching (CSFM). Rather than corrupting data with unstructured isotropic noise, CSFM formulates representation learning as the variance-minimizing inversion of a deterministic degradation curriculum across spectral, color, and illumination subspaces. By bounding trajectory variance with hard temporal style truncation, a capacity-constrained encoder is driven to ignore transient style artifacts and encode persistent content. Empirical evaluations across CIFAR-10, CIFAR-100, and STL-10 show that CSFM yields competitive discriminative transferability while preserving generative synthesis across both convolutional and vision transformer architectures. By avoiding the collapse pathologies of non-generative methods, CSFM forms a smooth latent space that outperforms standard optimal transport flows on linear probing and few-shot classification, while enabling coherent synthesis and trajectory interpolation. These results confirm that steering the physical dynamics of generative flows offers a scalable paradigm for learning representations that are simultaneously linearly separable and generatively invertible.
José Afonso, Mário Figueiredo
Instituto Superior Técnico, Lisboa, Portugal · Instituto de Telecomunicações, Instituto Superior Técnico, Lisboa, Portugal
Co-denoising pretrained representations such as DINO can substantially improve the training speed and quality of flow matching models, but it introduces a second denoising trajectory and requires carefully designed schedules. We propose a simpler alternative: predict the pretrained representation directly, then condition the model on its own prediction. This removes the need for a second ODE and any representation-specific denoising schedules, while retaining the benefits of representation guidance. Our approach converges substantially faster and achieves better generation quality as measured by FID score. On ImageNet, it outperforms the state of the art in latent space at 2x fewer epochs than prior methods; in pixel space, it improves FID over comparable prior methods by more than 20%. These results support a simple principle: do not denoise what you can predict. Our code is openly available at https://github.com/arijit-hub/dino_forcing.
Arijit Ghosh, Lucas Degeorge, Paul Couairon +3
ENPC, IP Paris · Ecole Polytechnique, IP Paris · AMIAD +1