Self-Regularized Flow Language Models

Theodoros Kouzelis; Spyros Gidaris; Nikos Komodakis

cs.LGOct 27, 2026

Self-Regularized Flow Language Models

Authors: Theodoros Kouzelis, Spyros Gidaris, Nikos Komodakis

Organizations: Archimedes, Athena RC · National Technical University of Athens · University of Crete · IACM-Forth

Abstract

We introduce SERF (Self-Regularized Flow Language Models), a simple self-supervised framework for improving continuous diffusion language models by exploiting the denoising trajectory itself. While continuous flow-based language models offer a promising alternative to autoregressive generation, their training objectives typically rely on supervision from clean target tokens, leaving the denoising trajectory underexploited as a learning signal. SERF addresses this limitation through noisy-to-clean self-distillation: an exponential moving average (EMA) teacher receives a cleaner version of the student's noisy input along the same interpolation path and provides additional supervision. We investigate two variants: SERF-L, which aligns the student's intermediate representations with deeper teacher representations, and SERF-P, which aligns their output token distributions, either at the student's output or at an early student layer. All variants augment the standard training objective without requiring external pretrained models or modifying the inference procedure. Experiments across three continuous language-model paradigms (one-hot FLM, latent ELF, and hyper-spherical S-FLM) demonstrate substantial improvements in training efficiency, generation quality, and few-step generation. In particular, SERF achieves up to 7.7x wall-clock training acceleration on OpenWebText, improves MAUVE by 24.3% and GSM8K accuracy by up to 28.8%, and matches baseline performance with up to 64x fewer sampling steps. These results establish noisy-to-clean self-distillation as an effective approach to improving continuous diffusion language models.

Figures & tables

Figure 1: Performance and efficiency gains of SERF . Improvements over FLM ( Lee et al., 2026 ) on OpenWebText ( Gokaslan and Cohen, 2019 ) and over S-FLM ( Deschenaux and Gulcehre, 2026 ) on GSM8K . Left: SERF reaches the baseline’s quality with substantially fewer training steps (see Fig. 4 ), achieving wall-clock acceleration despite its small additional computational cost (see Sec. A.4 ). Middle: Improves generation quality and reasoning accuracy at the same sampling budget (see Tab. 1 and Fig. 5 ). Right: Matches the baseline’s

1024

-step performance with only a fraction of the sampling steps (see Tab. 1 , Fig. 4 and Fig. 8 ). Sources for each value are listed in Tab. 2 .

Figure 2: Overview of SERF . In flow language models, the clean data lies at

\mathbf{x}_{1}

(one-hot token embeddings) and pure noise at

\mathbf{x}_{0}

. SERF corrupts

\mathbf{x}_{1}

at two noise levels along the same interpolation path using shared noise: the noisier input

\mathbf{x}_{s}

is fed to the student

f_{\theta}

, while the cleaner input

\mathbf{x}_{t}

(

t>s

) is fed to the EMA teacher

f_{\bar{\theta}}

, whose outputs are detached via stop-gradient. The student is supervised by the standard cross-entropy loss against the ground-truth one-hot target

\mathbf{x}_{1}^{l}

, plus a distillation loss weighted by

\lambda

, which takes one of two forms. Left: In Latent Distillation, ( SERF-L ) the hidden states of an early student block

k_{s}

are mapped through a lightweight projection head

g_{\theta}

and aligned with those of a deeper teacher block

k_{t}>k_{s}

using a per-token cosine distance. Right: In Probability Distribution Distillation ( SERF-P ), features from student block

k

pass through a small MLP and the teacher’s frozen head

o_{\bar{\theta}}

, giving token-wise distributions

\tilde{\mathbf{p}}_{\theta}^{l}

that are trained to match the teacher’s

\mathbf{q}_{\bar{\theta}}^{l}

via a cross-entropy loss; the student’s own output

\mathbf{p}_{\theta}^{l}

is trained with

\mathcal{L}_{\mathrm{FLM}}

Figure 3: Generated samples on OWT . Samples from FLM , and SERF-L , SERF-P k , trained for

1

M and

300

K steps and generated with

1024

sampling steps from the same initial noise. Errors are highlighted in bold . Both SERF variants produce notably more fluent text, whereas FLM exhibits grammatical errors and repetitions. We provide more examples of generated text in Appendix C .

		Sampling steps
Model	# Iters	$64$	$128$	$256$	$512$	$1024$
Best MAUVE ( $\uparrow$ )
FLM	$1$ M	$0.260$ $\pm 0.011$	$0.329$ $\pm 0.022$	$0.349$ $\pm 0.014$	$0.345$ $\pm 0.005$	$0.313$ $\pm 0.011$
SERF-P k	$300$ K	$\mathbf{0.341}$ $\pm 0.019$	$\underline{0.414}$ $\pm 0.026$	$\underline{0.399}$ $\pm 0.010$	$\underline{0.409}$ $\pm 0.026$	$\underline{0.388}$ $\pm 0.004$
SERF-L	$300$ K	$\underline{0.337}$ $\pm 0.009$	$\mathbf{0.435}$ $\pm 0.015$	$\mathbf{0.418}$ $\pm 0.017$	$\mathbf{0.423}$ $\pm 0.019$	$\mathbf{0.389}$ $\pm 0.005$
Gen. PPL at $H=5.44$ ( $\downarrow$ )

Table 1: Best MAUVE (

\uparrow

, top) on OWT over

\tau\in\{0.95,1.0,1.05\}

, where

\pm

is the std over 5 MAUVE seeds, and Gen. PPL (

\downarrow

, bottom) at the unigram entropy of OWT text (

H=5.44

), interpolated over each model’s temperature sweep. SERF-L and SERF-P k , trained for 300K steps, are compared against FLM trained for 1M steps. Best in bold , second best underlined . We further present the full MAUVE and Gen. PPL fronts in Fig. 8 .

Figure 4: Training convergence on OWT . SERF-L and SERF-P compared against FLM . At each iteration, we report the best MAUVE over

\tau\in\{0.95,1.0,1.05\}

and the Gen. PPL interpolated to the dataset entropy (see Sec. A.5 ), using

1024

sampling steps.

Figure 5: Left: GSM8K accuracy at

250

K training steps. Diffusion models at

1024

steps with

\tau=1

. Best overall underlined , best continuous diffusion bolded . ∗ Denotes our evaluation. Middle: GSM8K accuracy across sampling steps. SERF-L , SERF-P , and SERF-P k compared against S-FLM , all trained on TinyGSM ( Liu et al., 2023 ) for

250

K steps. We report the mean over 5 sample seeds. Right: Comparison with ELF on OWT . SERF-L compared against ELF-B , both trained for

5

epochs (

\sim

95

K steps) and sampled with

64

steps, sweeping the self-conditioning guidance scale

w\in\{0.5,1.0,1.5,2.0\}

Figure 6: Left: fixed (

\delta=0.8

) vs. random offset strategy for SERF-L and SERF-P , respectively. Right: The teacher’s output distribution supervises the student’s final layer ( SERF-P ) or an earlier block ( SERF-P k ,

k=2

). Both trained for

100

K steps on OWT .

Figure 7: Layer ablations for SERF-L and SERF-P k . Models trained for

50

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8: Mauve and Gen.PPL fronts for SERF-L and SERF-P k at 300K steps and for the baseline FLM at 1M steps. Curves obtained by sweeping the sampling temperature

\tau

Figure 9: Left: Regularization weight ablation for SERF-L and SERF-P . Right: Training convergence of SERF-L , SERF-P and SERF-P k against the S-FLM baseline, trained on TinyGSM and evaluated by GSM8K accuracy with

32

sampling steps.

Metric	Value	Comparison	Source
Left: wall-clock training acceleration
MAUVE	$\sim 7.7\times$	SERF-L vs. FLM	Fig. 4 (left)
Gen. PPL	$\sim 7.7\times$	SERF-L vs. FLM	Fig. 4 (right)
GSM8K Acc.	$\sim 1.4\times$	SERF-L vs. S-FLM	Fig. 9 (right),
Middle: relative improvement at the same sampling budget
MAUVE	$+24.3\%$	SERF-L vs. FLM	Tab. 1 (top)

Appendix

Table 2: Sources of the numbers in Fig. 1 . For each value, we list the compared models and where the underlying numbers are reported.

Figure 10: Generated samples on OWT . Samples from FLM (left) and SERF-L (right), all trained for

1

M and

300K

steps respectively. Text generated with

1024

sampling steps from the same initial noise. Errors are highlighted in bold .

Figure 11: Generated samples on OWT . Samples from FLM (left) and SERF-L (right), all trained for

1

M and

300K

steps respectively. Text generated with

1024

sampling steps from the same initial noise. Errors are highlighted in bold .

Figure 12: Generated samples on OWT . Samples from FLM (left) and SERF-P k (right), all trained for

1

M and

300K

steps respectively. Text generated with

1024

sampling steps from the same initial noise. Errors are highlighted in bold .

Figure 13: Generated samples on OWT . Samples from FLM (left) and SERF-P k (right), all trained for

1

M and

300K

steps respectively. Text generated with

1024

sampling steps from the same initial noise. Errors are highlighted in bold .

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