MeanFlowSE: One-Step Generative SE

• MeanFlowSE is a one-step generative speech enhancement method that learns an average-velocity field over finite intervals for direct denoising.
• It utilizes conditional mean flow formulations in both the complex STFT domain and latent SSL-conditioned spaces to reduce inference steps.
• Empirical results demonstrate competitive ESTOI, SI-SDR, and reduced RTF, highlighting its potential for real-time speech enhancement applications.

Searching arXiv for MeanFlowSE and closely related mean-flow speech enhancement papers. arXiv search results considered:

• "MeanFlowSE: one-step generative speech enhancement via conditional mean flow" (Li et al., 18 Sep 2025)
• "MeanFlowSE: One-Step Generative Speech Enhancement via MeanFlow" (Zhu et al., 27 Sep 2025)
• "MeanSE: Efficient Generative Speech Enhancement with Mean Flows" (Wang et al., 25 Sep 2025)
• "Compose Yourself: Average-Velocity Flow Matching for One-Step Speech Enhancement" (Yang et al., 19 Sep 2025)
• Foundational context: "Mean Flows for One-step Generative Modeling" (Geng et al., 19 May 2025)

MeanFlowSE denotes a set of one-step generative speech enhancement formulations that adapt the MeanFlow idea of learning an average-velocity field over finite time intervals rather than only an instantaneous velocity field. In speech enhancement, the motivation is explicit: multistep diffusion and flow-matching systems learn local dynamics and therefore depend on iterative ODE or reverse-time solvers, whereas MeanFlowSE aims to predict a finite-interval displacement that can be applied in a single update. On arXiv, the term is presently ambiguous rather than singular, because it appears in both “MeanFlowSE: one-step generative speech enhancement via conditional mean flow” (Li et al., 18 Sep 2025) and “MeanFlowSE: One-Step Generative Speech Enhancement via MeanFlow” (Zhu et al., 27 Sep 2025), two related but architecturally distinct systems.

1. MeanFlow basis and the speech-enhancement rationale

The conceptual basis of MeanFlowSE is the MeanFlow formulation introduced for one-step generative modeling, where the learned object is the average velocity

$$u(z_t,r,t) \triangleq \frac{1}{t-r}\int_r^t v(z_\tau,\tau)\,d\tau$$

rather than the instantaneous velocity $v(z_t,t)$. This changes inference from numerical integration of a local field to a finite jump,

$z_r = z_t - (t-r)\,u(z_t,r,t),$

and, in the one-step case, to

$x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$

The original MeanFlow paper frames this as learning a finite-interval transport quantity that is better aligned with one-step generation than an infinitesimal tangent field (Geng et al., 19 May 2025).

Speech enhancement is an especially natural target for this reformulation because recent generative SE systems are constrained less by unconditional synthesis difficulty than by inference latency. Both MeanFlowSE papers state this bottleneck directly: diffusion- and flow-matching-based SE methods typically rely on multistep inference, and the need to numerically integrate or iteratively denoise is the main obstacle to real-time deployment. MeanFlowSE therefore reinterprets enhancement as a one-step conditional transport problem, with noisy speech providing the conditioning signal and the learned average-velocity field providing the entire denoising displacement in a single evaluation (Li et al., 18 Sep 2025, Zhu et al., 27 Sep 2025).

2. Conditional mean flow in the complex STFT domain

The formulation in “MeanFlowSE: one-step generative speech enhancement via conditional mean flow” is built directly in the complex STFT domain and is explicitly conditional on the noisy observation $y$. It defines a dual linear–Gaussian conditional path

$$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$

with

$$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$

Here $x_1$ is clean speech and $y$ is noisy speech. Differentiating the path yields the on-path conditional instantaneous target

$$v_t(x_t\mid x_1,y) = \mu_t' + \sigma_t' z = \frac{\sigma_t'}{\sigma_t}(x_t-\mu_t)+\mu_t'.$$

The mean-flow object is then defined as

$v(z_t,t)$0

with diagonal consistency

$v(z_t,t)$1

A central identity follows by differentiating $v(z_t,t)$2: $v(z_t,t)$3 where the total derivative along the trajectory is

$v(z_t,t)$4

This converts an interval integral into a local training rule. The network $v(z_t,t)$5 is trained by a JVP-based first-order target,

$v(z_t,t)$6

with $v(z_t,t)$7 in the reported experiments, and the loss

$v(z_t,t)$8

At $v(z_t,t)$9, the correction vanishes and the objective reduces to conditional flow matching.

Inference is displacement-based rather than solver-based. The general reverse-time update is

$z_r = z_t - (t-r)\,u(z_t,r,t),$0

and the single-step form is

$z_r = z_t - (t-r)\,u(z_t,r,t),$1

The implementation uses an NCSN++ U-Net with self-attention. Inputs are $z_r = z_t - (t-r)\,u(z_t,r,t),$2 concatenated along channels; conditioning uses Gaussian Fourier embeddings of the primary time $z_r = z_t - (t-r)\,u(z_t,r,t),$3 and span $z_r = z_t - (t-r)\,u(z_t,r,t),$4. The paper also reports several stabilizers: automatic differentiation for derivatives, a centered finite-difference fallback, stop-gradient on the target, per-sample $z_r = z_t - (t-r)\,u(z_t,r,t),$5 clipping for the Jacobian term, warmup of the mean-branch weight to $z_r = z_t - (t-r)\,u(z_t,r,t),$6, annealing the span-sampling exponent from $z_r = z_t - (t-r)\,u(z_t,r,t),$7 to $z_r = z_t - (t-r)\,u(z_t,r,t),$8, and injection of $z_r = z_t - (t-r)\,u(z_t,r,t),$9 in $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$0 of batches (Li et al., 18 Sep 2025).

3. SSL-conditioned latent MeanFlowSE

The second MeanFlowSE paper relocates enhancement from the STFT domain to a pretrained latent space and makes SSL conditioning central. Clean speech is encoded by the WaveVAE from KALL-E into 256-dimensional latents at 25 Hz, while noisy speech is represented by WavLM-Large features. All 24 WavLM-Large transformer layers are fused through a trainable weighted sum with softmax normalization. The generative core is a DiT with $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$1 transformer layers, 8 attention heads, hidden size 512, and feed-forward dimension 2048 (Zhu et al., 27 Sep 2025).

Its MeanFlow equations are the standard average-velocity relations: $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$2 with direct one-step transport written first as

$x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$3

and operationally, at inference, as

$x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$4

The enhanced waveform is then reconstructed by the VAE decoder,

$x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$5

Training predicts $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$6 from interpolated latent $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$7, noisy SSL conditioning $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$8, positional encodings, and time embeddings $x = z_0 = \epsilon - u_\theta(\epsilon,0,1).$9 and $y$0. The reported objective is an adaptive weighted squared error,

$y$1

where

$y$2

The paper states that the target average velocity is derived analytically from $y$3 and $y$4, and that MeanFlow is implemented with an autograd-based JVP formulation.

A defining architectural claim is that SSL conditioning is superior to conditioning on noisy VAE latents. The ablation named MeanFlowSE$y$5 keeps the same one-step backbone and runtime but degrades both perceptual and semantic metrics, including a simulated-set WER increase from $y$6 to $y$7. This assigns a specific role to the WavLM representation: it is not an auxiliary loss target, but the principal noisy-speech guidance signal for the latent transport model (Zhu et al., 27 Sep 2025).

4. Position within the broader mean-flow speech-enhancement literature

MeanFlowSE belongs to a broader 2025 line of SE work that replaces instantaneous-flow modeling with interval-level transport quantities. The immediate baseline is FlowSE, which remains a conditional flow-matching method with an instantaneous velocity field $y$8 and forward ODE integration from $y$9. Its conditional path is centered on the noisy speech through

$$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$0

but inference still requires Euler integration with $$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$1 steps (Lee et al., 9 Aug 2025).

MeanSE moves closer to the first MeanFlowSE formulation. It defines

$$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$2

and uses the one-step rule

$$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$3

Its reported training recipe requires flow field mix-up, initialization from a trained FlowSE checkpoint, and interval curriculum learning, which the paper presents as necessary because directly regressing mean flows from scratch is unstable (Wang et al., 25 Sep 2025).

COSE occupies a different point in the design space. It keeps the average-velocity target for one-step SE but replaces MeanFlow’s JVP-based differential identity with a velocity composition identity derived from ODE semigroup structure: $$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$4 The paper’s core claim is that this eliminates JVPs while preserving theoretical consistency and reduces training cost by $$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$5 and sampling cost by up to $$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$6 without compromising enhancement quality (Yang et al., 19 Sep 2025).

Taken together, these papers show that “mean flow” in SE is not a single implementation but a methodological direction: interval-average velocity, one-step displacement, and the replacement of ODE integration by direct transport.

5. Reported empirical performance

The two MeanFlowSE papers report on different benchmarks and use different representations, so their metrics are not directly interchangeable. This suggests that MeanFlowSE is better understood as a design family than as a single benchmarked system (Li et al., 18 Sep 2025, Zhu et al., 27 Sep 2025).

Variant	Benchmark	Reported result
MeanFlowSE (Li et al., 18 Sep 2025)	VoiceBank-DEMAND	$$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$7 NFE, ESTOI $$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$8, SI-SDR $$\mu_t = (1-t)\,x_1 + t\,y,\qquad \sigma_t = (1-t)\,\sigma_{\min} + t\,\sigma_{\max},$$9, BAK $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$0, RTF $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$1
MeanFlowSE (Zhu et al., 27 Sep 2025)	Simulated DNS test	WER $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$2, RTF $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$3, $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$4M parameters
MeanFlowSE (Zhu et al., 27 Sep 2025)	DNS blind test, with reverb	SIG $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$5, BAK $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$6, OVRL $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$7

On VoiceBank-DEMAND, the conditional-mean-flow variant reports the strongest ESTOI, SI-SDR, BAK, and SpkSim in its comparison table, together with the lowest RTF. Its OVRL score $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$8 is slightly below the Schrödinger Bridge value $$x_t = \mu_t + \sigma_t z,\qquad z\sim\mathcal N(0,I).$$9, but it reaches that regime with $x_1$0 NFE rather than $x_1$1 (Li et al., 18 Sep 2025).

On the DNS blind and simulated tests, the latent SSL-conditioned variant reports SOTA-level perceptual quality and competitive intelligibility. On the simulated test set it has the best WER, lowest RTF, and smallest parameter count among the listed generative baselines. Against its own flow-matching ablations, MeanFlowSE trades a small residual quality gap to FM(100) for a substantially lower RTF: $x_1$2 versus $x_1$3 (Zhu et al., 27 Sep 2025).

6. Misconceptions, ambiguity, and open questions

A common misconception is that MeanFlowSE names one canonical architecture. Current arXiv usage does not support that reading: one MeanFlowSE is an STFT-domain conditional mean-flow model with JVP-based first-order correction, and another is an SSL-conditioned latent DiT with a WaveVAE decoder. A second misconception is that MeanFlowSE is simply FlowSE run with fewer steps. FlowSE still learns an instantaneous vector field and integrates an ODE, whereas MeanFlowSE variants explicitly learn average-velocity fields for one-step displacement or latent refinement. A third misconception is that one-step transport removes technical complexity. The reported systems still rely on derivative handling, span sampling, clipping, pretrained SSL or VAE components, and carefully chosen conditioning schemes. Related work such as COSE further indicates that JVP overhead remains an active optimization target. These points are all visible across the MeanFlowSE, FlowSE, MeanSE, and COSE papers (Lee et al., 9 Aug 2025, Li et al., 18 Sep 2025, Zhu et al., 27 Sep 2025, Wang et al., 25 Sep 2025, Yang et al., 19 Sep 2025).

The open issues are similarly concrete. The conditional-mean-flow paper explicitly lists its use of a linear–Gaussian path and first-order derivative estimation as a limitation and points to more flexible or data-driven paths, higher-order corrections, and evaluation under real-world conditions. The latent SSL-conditioned paper identifies further improvement of speech quality, adaptation to low-latency streaming, and extension to full-band scenarios as future directions. MeanSE adds a practical warning: directly learning mean flows from scratch can be unstable without flow field mix-up and interval curriculum. A plausible implication is that MeanFlowSE should presently be read less as a finished canonical recipe than as a rapidly consolidating research program for one-step generative speech enhancement.