Decoupled DMD: CFG Augmentation as the Spear, Distribution Matching as the Shield
Authors: Dongyang Liu
Peng Gao
David Liu
Ruoyi Du
Zhen Li
Qilong Wu
Xin Jin
Sihan Cao
Shifeng Zhang
Steven HOI
Hongsheng Li
Venue: ICLR 2026 Poster (2026)
Keywords: Diffusion Model
Diffusion Distillation
Primary area: generative models
TL;DR: Conventional wisdom holds that DMD works by matching distributions. We decouple the objective and find this is incorrect. The true "engine" of distillation is CFG Augmentation (CA), while Distribution Matching (DM) is a "regularizer" for stability.

Abstract: Diffusion model distillation has emerged as a powerful technique for creating efficient few-step and single-step generators. Among these, Distribution Matching Distillation (DMD) and its variants stand out for their impressive performance, which is widely attributed to their core mechanism of matching the student's output distribution to that of a pre-trained teacher model. In this work, we challenge this conventional understanding. Through a rigorous decomposition of the DMD training objective, we reveal that the primary driver of few-step generation is not the distribution matching term, but a previously overlooked component we identify as \textit{\textbf{C}FG \textbf{A}ugmentation} (\textbf{CA}). We demonstrate that this term acts as the core "engine" of distillation, while the \textbf{D}istribution \textbf{M}atching (\textbf{DM}) term functions as a "regularizer" that ensures training stability and mitigates artifacts. We further validate this decoupling by demonstrating that while the DM term is a highly effective regularizer, it is not unique; simpler non-parametric constraints or GAN-based objectives can serve the same stabilizing function, albeit with different trade-offs. This decoupling of labor between CA and DM also allows a more principled analysis of the properties of both terms, leading to a more systematic and in-depth understanding. This new understanding enables us to propose principled modifications to the distillation process, such as decoupling the noise schedules for the engine and the regularizer, leading to further performance gains.

Published as a conference paper at ICLR 2026
DECOUPLED DMD: CFG AUGMENTATION AS THE SPEAR, DISTRIBUTION MATCHING AS THE SHIELD
Dongyang Liu 1.2
Peng Gao 1.49 David Liu
Ruoyi Du'
Zhen Li' Qilong Wu
Xin Jin
Sihan Cao Shifeng Zhang'
Steven HOI
Hongsheng L22.3,
Tongyi Lab, Alibaba Group MMMLa,, CUHK
SCPII under InnoHK
1 Shenzhen Institutes of Advanced Technology. Chinese Academy of Sciences
jingpeng. gpdalppliaaaeaa satallibba-iinne inc. com @hsli@ee mahk.eduu hk
Q https::////. //g::///ttt / wtwpgg...t.oooooooooooooommmoot www.oongo//iiiooceecoo -MAT
-MATT Image
ABSTRACT
Diffusion model distillation has emerged as a powerful technique for creating efficient few-step and single-step generators. Among these, Distribution Matching Distillation (DMD) and its variants stand out for their impressive performance, which is widely attributed to their core mechanism of matching the student's output distribution to that of a pre-trained teacher model. In this work, we challenge this conventional understanding. Through rigorous decomposition of the DMD train- ing objective, we reveal that in complex tasks like text-to-image generation, where CFG is typically required for desirable few-step performance, the primary driver of few-step distillation is not the distribution matching term, but a previously over- looked component we identify CFG Augmentation (CA). We demonstrate that this term acts as the core "engine" of distillation, while the Distribution Matching (DM) term functions more as "regularizer" that ensures training stability and mit- igates artifacts. We further validate this decoupling by demonstrating that while the DM term a highly effective regularizer, it not unique; simpler non-parametric constraints or GAN-based objectives can serve the same stabilizing function, albeit with different trade-offs. This decoupling of labor between CA and DM also allows more principled analysis of the properties of both terms, leading to a more sys- tematic and in-depth understanding. This new understanding enables us to propose principled modifications to the distillation process, such decoupling the noise schedules for the engine and the regularizer, leading to further performance gains.
INTRODUCTION
Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020) have rapidly risen to prominence in generative modeling, achieving state-of-the-art performance and producing images of unprecedented quality and diversity. This success has sparked widespread interest across both academia and industry. However, the power of these models comes at significant cost: their iterative sampling process, often requiring dozens to hundreds of neural network evaluations, is computationally expensive and slow, hindering their use in real-time applications.
To address this limitation, flurry of research has focused on converting the original diffusion model into few-step generator. Typical technical routes include direct distillation (Liu et al., 2022), where the student is expected to replicate the trajectory of the teacher: consistency distillation (Song et al., 2023), which enforces self-consistency along the sampling trajectory; and adversarial distil- lation (Sauer al., 2024b), which leverages an adversarial objective to match the student's output distribution to target, showing impressive results in high-resolution synthesis.
Among these diverse approaches, score-based distillation, notably represented by Diff-Instruct (Luo et al., 2023b), Distribution Matching Distillation (DMD) (Yin et al., 2024b), and other variants (Yin et al., 2024a; Chadebec et al., 2025), has been recognized as exceptionally promising. Its advantages twofold: not only does it achieve oftte-of-thearr performance, but it is also underpinned by an elegant theoretical framework. Specifically, the method is framed as minimizing an Integral Leibbeck-Leibler (IKI.) divergence (Luo al., 2023b) between the student's output distribution

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Scond
Scond
real
Sef
prepared &
re-noised x-
Real Modell
uncond
VDLDMD
fale Sond
real
(a) Traditional View
condition
Real Model
Scand
fake Scond
CA: dig
Generatur
real
LoD
D.M greal
Fake Model
Go
condd
fake
(b) Our View
Figure 1: Two perspectives on the DMD algorithm. (a) The conventional view, which treats the use of CFG as heuristic relaxation of the theoretical framework, with the algorithm' success solely attributed to this (relaxed) distribution matching mechanism. (b) Our proposed decoupled view, where the objective is combination of two distinct mechanisms: CFG Augmentation (CA) engine that drives the few-step conversion, and Distribution Matching (DM) regularizer-whiee strictly adheres to the theoretical derivation (Eq. 1) that ensures training stability.
(Ptake) and the teacher's target distribution (Preal):
LIKL (Preal Plake) f.
TKT (preal- ll Piake, dr.
(1)
In practice, the gradient of this objective is estimated using pair of "real" (teacher) and "fake" (student-tracking models, making the training process feasible.
However, a dark cloud has loomed over the interpretation of this elegant method: the use of Classifier-Free Guidance (CFG) (Ho & Salimans, 2022) on the real model. According to the theoretical derivation, the ideal estimator for the target real score should be the prediction from the real model itself, with no involvement of CFG. However, empirical evidence overwhelmingly shows that complex tasks like text-to-image, DMD-like methods yield good results only with high CFG scale. Even if we were to boldly assume-da an assumption we find to be insufficiently grounded that CFG somehow produces higher-quality substitute for the original score, the asymmetric application of CFG, in which only the real model but not the fake model is equipped with CFG, still creates a stark inconsistency between theory and practice. Overall, the usage of CFG breaks the integrity of the original, rigorous theoretical derivation of matching two distributions.
This strongly suggests that the current understanding of DMD's success is likely incomplete inaccurate. In this paper, we aim to redefine the understanding of how DMD and similar algorithms work. Through rigorous decomposition of the practical DMD training objective that utilizes real score CFG, we reveal that its effectiveness is not driven by a single mechanism, but by a clear division of labor between two distinct components:
1. CFG Augmentation (CA): A previously overlooked term that directly applies the CFG signal to the student's output. We demonstrate that this component acts as the core engine of distillation, responsible for converting multi-step model into high-quality few-step generator.
2. Distribution Matching (DM): A mechanism that perfectly aligns with the theoretical derivation (Eq. 1). While existing works have proved its independent distillation capability in simple tasks like low-resolution CIFAR (Luo et al., 2023b), show that for complex tasks, its primary function converts more to powerful regularizer that ensures training stability and mitigates artifacts.
This decoupled framework challenges the prevailing narrative and provides more accurate ex- planation for the success of DMD-like methods. We substantiate our claims through a series of carefully designed experiments, including independent investigations of the effect of each component, and demonstrating that the DM regularizer, while highly effective, can be conceptually replaced complex GANs. This explicit decoupling also enables
by simpler statistical constraints
2

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Published as a conference paper at ICLR 2026
more principled and in-depth analysis of the properties and inner workings of each component. Finally, armed with this deeper understanding, we propose principled improvement by proposing decoupled renoising schedules for CA and DM, respectively, leading to further performance gains, and demonstrating the practical value of our new perspective.
2 RELATED WORK
Few-Step Diffusion Distillation aims to reduce the inference cost of diffusion models. Trajectory- matching approaches train a student model to replicate the teacher's sampling path in fewer steps (Liu et al., 2023; Zhu et al., 2024; Kim et al., 2024; Frans et al., 2024; Salimans & Ho, 2022; Meng et al., 2023), with consistency distillation as renowned branch (Song al., 2023; Kim al., 2023; Lu & Song, 2024; Wang et al., 2024; Ren et al., 2024). Another prominent direction is GAN-based distillation (Sauer et al., 2024b;a; Lin et al., 2024). which leverages an adversarial objective match the student's 's output distribution with the teacher's 's or with real data.
Score-based Distillation was initially proposed for 3D generation (Poole al., 2022; Wang et al., 2023). Diff-Instruct (Luo et al., 2023b) pioneered its application in few-step diffusion distillation, and DMD (Yin et al., 2024b) was among the first to successfully apply this principle to aarge-scale text-to-image models. Following works have explored different distribution metrics (Zhou et al., 2024b;a) or combining this principle with other distillation paradigms (Yin et al., 2024a; Chadebec et al., 2025; Luo et al., 2024). Notably, the adoption of CFG in real score is common practice among these works, but this choice is rarely officially discussed. An exception is (Luo, 2024), which models the CFG term role of this CFG term during distillation and to reveal its dominance in multi-to-few-stee conversion.
extra reward function after distillation. We are the first to decouple the
3 REVISITING AND DECOMPOSING DMD
The goal of Distribution Matching Distillation (DMD) is to train a student generator, denoted as Gg, to emulate the output distribution of a pre-trained, frozen teacher diffusion model in few-step or even single-step inference process. The training is guided by minimizing a loss function, Eq. 1, whose gradient with respect the generator's parameters 0 can be estimated by:
V VoLDMD theory = -2,,,, [-
[Go(21)
cond (x.)
Scond (x.,)
(2)
00
In this paper, we follow the flow matching notations (Lipman et al., 2022) and define t= 0 with pure noise and t = 1 with clean data. 2 denotes the prepared generator input at noise level t. For single-step generation. t is O and 2, is random noise; for few-step generation, 2, can be obtained by going through the previous steps, a technique called "backward simulation" (Yin et al., 2024a). The generator Go takes 2, and makes the image prediction (z)z,), which is then renoised to x, with sampled noise level т. After renoising, Iy would be fed to two diffusion models for score estimates: real the "real score" estimated by the original multi-step teacher model; and s cond the "fake" score estimate from an auxiliary "fake" model that is trained concurrently on the generator's ' outputs. The subscript "cond" indicates the score conditioned on a text input. Pseudo-code provided in Sec. C
However, while Eq. 2 proved to be effective on simple generation tasks, its performance on complex tasks like text-to-image usually unsatisfactory, and a subtle modification required:
[-
(Go(z.)
LDLD = B2,,,
real Scfg
(x,)
fake sonnd
(x.)
(3)
08
The only difference between Eq. 2 and Eq. 3 is that the real score scal is replaced with real "ig
where
real Pelg
(x-)
Puncond (x+) (ccal (x+))
real
real annoona (x+))
(4)
real and sinsond are the conditional and unconditional scores from the real model, respectively, and a is the CFG guidance scale (typically a >> 1). Despite the introduction of discrepancy between theory and practice, this modification empirically yields substantially better results. Interestingly, this substitution has been largely overlooked in prior literature, often dismissed as a mere implemen- tation detail rather than fundamental deviation from the original theory. However, we will show
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CA
CA DM
DM
CA
CA + DM
DM
Stepe
1000 Stege
Strrps
78000 Steps
1000 SAxpa
4000
1:00 Steps
HERD
Stope
Revani
Reward
rBs v2.1
Step SDXL
Slup
Figure 2: Ablation study on the roles of CFG Augmentation (CA) and Distribution Matching (DM).
Numerical indicators are evaluated 1k sampled prompts from COCO-1Ok (Lin al., 2014).
that the seemingly minor CFG detail actually signifies a fundamentally different mechanism independent to distribution matching.
For clarity, in the rest of the paper, we use the acronym "DMD" specially refer in in-practice-used and CFG-involved algorithm as defined in Eq. 3. In contrast, we use the term "Distribution Matching" its abbreviation "DM" to refer exclusively the theoretical principle matching two distributions, which strictly adheres to the formulation in Eq. and Eq. 2. We will show that the success of DMD from the cooperation of two different mechanisms, with Distribution Matching playing crucial, yet secondary, role as regularizer rather than the primary distillation engine.
3.1 DECOMPOSING THE DMD GRADIENT
To serutinize the underlying mechanisms the DMD algorithm, we begin by substituting the definition of Classifier-Fres Guidance (Eq. 4) into the DMD gradient formula (Eq. 3):
4D4DMD = | |eall (x, ) /rral real (ooodd (x+)
"uncond (x+)))
fake "cond (x.)) 8Go
(5)
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With simple rearrangement, decompose Eq. 5 into two distinct components:
DMCDMD =
Cou (x+)
"cood
(x+)
+(a
cond
gtcal sencodd (x+))
(G)
00
(6)
A (Distribation Matching)
Apd (CFG Augmentation)
This decomposition reframes the DMD objective as sum two terms:
1. Distribution Matching (DM, A reul-fake): The first term, s
Lake -oodd
strictly aligns with theoretical
deduction matching two distributions (Eq. and 2).
2. CFG Augmentation (CA, A The second term, (a sstald
s directly applies
scaled CFG signal as gradient to the student's output. This component was typically overlooked.
This separation motivates an ablation study to isolate the true contribution of each component. We
investigate three training configurations: (1) the full DMD objective (A real-fake + dgg (2) CFG
Augmentation only (A real), and (3) Distribution Matching only (A rake.
3.1.1 ABLATION STUDY: ENGINE VS. REGULARIZER
As illustrated Fig. our experiments reveal a clear division of labor between the two components. Training with CA alone is remarkably effective at converting the multi-step model into few-step generator. Besides, the generated results also demonstrate high similarity in content to the full DMD objective, indicating the dominant role of the CA term in DMD loss. In contrast, even though improper to conclude that the DM term is totally incapable of doing the multi-step to few- step conversion (since in the 4-step experiment it indeed makes relatively reasonable images), significant performance gap exists towards the CA setting, as indicated by both image visualizations and numerical indicators (Image Reward (Xu et al., 2023) and HPS v2.1 (Wu et al., 2023)).
However, we also observe that training with CA alone unsustainable. While initially effective, the generated images progressively suffer from artifacts such as over-saturation and high-frequency noise, eventually leading to training collapse. The introduction of the Distribution Matching term eliminates these issues, enabling stable training over extended periods and yielding higher-quality final results. These empirical findings lead to two fundamental conclusions:
1. CFG Augmentation is the engine for few-step conversion. The ability of the distilled generator to produce high-quality samples in a few steps is almost entirely attributable to the A term.
2. Distribution Matching is regularizer for training stability. The A real-fake term, while not the primary driver distillation, plays crucial role as a regularizer that prevents the training process from diverging and ensures the quality of the final output.
This insight fundamentally challenges the prevailing understanding of DMD-like methods: the conversion to a few-step generator not primarily an act of matching distributions but rather a direct consequence of "baking the CFG pattern into the student generator's predictions (we elaborate on this point in Sec. B), which irrelevant to the fake model.
3.2 DISTRIBUTION MATCHING: A GOOD, BUT NOT THE ONLY, REGULARIZER
To further validate the aforementioned division between engine and regularizer, we investigate whether alternative regularization schemes can effectively stabilize the CFG Augmentation (CA) engine. This section demonstrates that even simple non non-paramttric statistical constraint can prevent training collapse, thereby substantiating the role of Distribution Matching (DM) as a regularizer. Concurrently, we highlight that DM is an exceptionally well-suited regularizer for this task, exhibiting clear advantages over both simpler non-parametric methods and more complex GAN-based approaches.
Non-Parametric Mean-Variance Variance Regularization. As shown Fig. 3, training with the CA engine leads to monotonic increase in the variance of generated images, finally reaching unreasonably large values. This inspires us to design the simplest regularization term of constraining the mean and variance of the generator's output. Specifically, loss that aligns the imr- mean and variance o² of the student's output Go (22) with target statistics (Parget, t. For SDXL experiments, we use Marget 0.075 and d Tenget 0.81, which
apply a Sullback-Leibler (KL) divergence
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Mean
Shardand Deviation
Image Reward
05
Ntarv/ar Segrasees
Otertaudion Vaacing
GW
Figure 3: CFG Augmentation with different regularizers. Image Reward and HPS v2.1 evaluated on IK sampled prompts from COCO-10k. Setting: 4-step SDXL. See Fig. 8 for visualized samples.
the averaged statistics of sampled real data. For a batch of B generated images, the loss is defined as:
o? + (/4 Itarget)
of
KL
log furget
B
2-1
of
Tugeet
where of) are the mean and variance of the i-th generated image.
As shown in Fig. 3 and Fig. 8, this simplest non-parametric regularization proves remarkably effective at stabilizing the training process, allowing the CA engine to operate durably, keeping the quality relatively high level. This result strongly reinforces the hypothesis that the primary role of the DM term is a regularizer. However, the final image quality, while stable, falls noticeably short of that achieved with DM. This suggests that the artifacts induced by the CA engine are more complex than what can be captured by wwean&variane, alone.
indicators
GAN-based Regularization A more powerful candidate for regularization is GAN discriminator, technique already employed in several diffusion distillation works (Yin et al., 2024a; Lin et al., 2025). Following existing methods (Sauer et al., 2024b), we use discriminator initialized from the weights of the pre-trained teacher model. Experiments (Fig. 3) confirm that GAN can indeed function as a regularizer, effectively controlling image variance and climinating certain artifacts. However, GAN requires image data during the distillation process. Besides, the approach introduces significant challenges in training stability, as the training still collapsed after 4k iterations.
Our investigation suggests that while distribution matching is not the only possible regularizer, it represents a sweet spot- offe-infering a more powerful corrective signal than simple statistical constraints, while being substantially more stable and less complex than GANs. The comparison suggests trade-off between stability and potential performance. The increasing complexity from statistical constraints GANs correlates with decreasing training robustness, which echoes the claim in Diff- Instruct (Luo et al., 2023b) that score- matching can be viewed as a more stable alternative to GANs, especially when the distributions have disjoint supports. Conversely, greater complexity may offer higher performance ceiling. This aligns with practices VAE training (Rombach et al., 2021; 2022) or advanced few-step distillation (Lin et al., 2025), where models often first trained with stable objective before being fine-tuned with a GAN loss to achieve peak performance.
4 MECHANISTIC ANALYSIS OF CA AND DM
The decomposition of the DMD objective into a CA engine and a DM regularizer enables an in depth exploration of their respective inner workings. This section aims to answer two fundamental questions: first, how exactly does the CA engine drive the multi-step to few-step conversion? And second, by what mechanism does the DM regularizer ensure the stability of this process?
4.1 DISSECTING THE CA ENGINE: THE ROLE OF THE RE-NOISING SCHEDULE
To understand the working mechanism of the CA engine, we investigate central question: How does the choice of re-noising timestep J influence the eff'ctt of CA? Since 7 determines the noise level which the CFG signal computed, serves powerful probe into the engine's 's behavior.
To isolate this effect, we design an experiment where a single-step generator is trained using only the CA term (Auel) We then systematically vary the sampling range of the re-noising timestep т, starting from the noisiest end of the spectrum and gradually expanding towards cleaner timesteps.

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cc [0,0.05]
[.,
TE [0.0.3]
re [0,
re [0.7.10)
Gx(a.)
Yoond
Figure 4: (a) Visualization on the effect of re-noising timestep F in CFG Augmentation (CA). The generator is trained with CA alone. In our notation, 7 corresponds to pure noise and 7 1 to clean data. (b) Illustration of the DM corrective mechanism. The generator is trained with CA alone, while the fake model keeps training on the generator's output as DMD.
Results in Fig. (a) reveal a clear and consistent pattern. When restricted a noisy range (e.g.. [0.0, 0.05)), the CA engine primarily enhances low- fow-frequency information, such as broad color blocks and overall composition. As the range r expands to include cleaner timesteps, the generated images progressively gain richer, higher-frequency details, like sharp edges and fine textures. This leads to crucial conclusion: the CA engine, when applied at a specific noise level т, primarily enhances the image content corresponding to that level. This conclusion is further supported by the fact that the training collapses when r is restricted to clean timesteps only ([0.7, 70.7,1 1.0)): high- high-frequency details meaningless if low-frequency general structure has not yet been determined.
This finding has a critical implication for multi-step generation. Consider a generator at step t operating on input 2,, which already contains resolved information for noise levels below 1. Is still necessary, or even detrimental, to apply CA with a re-noising range containing 7 < /? Our analysis suggests this would be redundant, potentially over-enhancing already established features and leading to artifacts. We therefore hypothesize that an optimal CA schedule should act as focused engine, concentrating its power on the remaining, unresolved aspects of the image by constraining its re-noising schedule to r > f. Experimental validation is provided in Sec. 4.3.
4.2 UNDERSTANDING THE DM REGULARIZER: A CORRECTIVE MECHANISM
Having established CA as the engine, we now turn to the DM regularizer and ask: How does counteract the artifacts introduced by CA and ensure training stability?
To gain insight into this corrective mechanism, we design specific diagnostic experiment. We continue train the generator using only the CA engine, setting we know is unstable and produces artifacts. However, we introduce an auxiliary "fake" model as a non-interfering observer. This fake model trained concurrentyy on the generator's outputs-just as in standard DMD its score estimate is not used to update the generator. This setup allows us to witness when artifacts occur, how potential DM gradient (steal - -okee) would act to correct them.
Fig. 4 (b) offers an informative observation. The image generated by the CA-only generator exhibits clear high-frequenc, checkerboard artifacts. When this artifact-laden image is re-noised and fed to the two score models, the artifact is conspicuously absent in the prediction from the frozen real model, yet it persists in the prediction from the observer fake model. This occurs because the fake model, by tracking the generator's ' output distribution, has learned to replicate its characteristic failure modes. Consequently, in the DM gradient, the artifacts present in the fake prediction (s (s form negative term. Applying this gradient to the generator's 's output would thus encourage a change that actively cancels out these artifacts. This provides concrete illustration of DM's corrective mechanism.
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Table Ablation on different re-noising schedule configurations with Lumina- Lumina-Image-2.0. Detailed results on the HPS benchmarks are provided in Tab. 16 and 17
DPG Bench
HPS v2.1
HPS V3
Model
Global
Entity
Attribute
Relation
Other
Overall
Overall
Overall
Original (50 steps)
84.50
91.20
94.42
86.34
87.20
30.20
9.62
Orea 7MM E [0, I] (DMD)
80.22
90.45
90.47
89.36
91.36
83.90
30.61
10.34
@rea 1|: TDM [0. 1]
91.88
89.03
90.08
89.51
88.85
83.77
30.69
10.32
TrC f,
93.47
90.18
90.94
89.37
90.71
85 64.64
31.71
11.08
ΦrCa 1, [0. 1]
91.40
91.62
91.18
91.93
91.98
85.85
32.29
11.59
Figure 5: Un-cherry-pickee qualitative comparison of different re-noising schedule configurations. Top row: @ Decoupled-Fuit TCA. TOM [0, 1]. Middle row: @ Coupled- TCA. TDM > t. Bottom row: 4 our proposed Decoupled Hybrid, Hecoud,ed-Hyyrid, TCA TDM [0, 1].
This understanding also clarifies the role of the re-noising timestep 7 within the DM regularizer: controls the scope of correction. A large 7 (cleaner image) allows the real and fake scores to diverge primarily subtle, high-frequency details. In contrast, small т (noisier image) destroys most details. forcing the scores to diverge on more fundamental, low-frequency elements like composition and color. This gives the DM regularizer an opportunity correct global issues.
This leads to our final hypothesis regarding the optimal renoising schedule for DM in few-step setting. Even late-stage generation steps, which primarily add high-frequency details, can still suffer from low-frequee www-frequency artifacts like color oversaturation, either inherited from previous steps or induced by an imperfect CA schedule. To address these global issues, the DM regularizer requires a global perspective. Therefore, we propose that the optimal DM schedule is different from that of CA: DM should function as a comprehensive regularizer, always spanning the full noise range (TDM [0, 1)), irrespective of the generator's current timestep
4.3 VALIDATING THE DECOUPLED SCHEDULE HYPOTHESIS
Our mechanistic analysis in Sec.4.1 and Sec.4.2 has led to a central hypothesis: for optimal few-step distillation, the CA engine and the DM regularizer require distinct, decoupled re-noising schedules. Specifically, we proposed that the CA schedule should be constrained (Tca t) to act as focused engine, while the DM schedule should remain global (7DM [0. 1]) serve as a comprehensive regularizer. In this section, we empirically validate this proposal.
To facilitate this investigation, first generalize the DMD gradient (Eq.6) a 7-decoupled form. This allows to assign independent re-noising schedules, TCA and TDM. to the CA and DM compo- nents, respectively. The resulting "decoupled DMD" (d-DMD) gradient formulated as:
V.CADMD = -0(((s( ((1ral (X -
fake "cond (x )) + (a 1) real cood (xrrx) uuncond (xrca)) 8Go(
.real
(8)
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Table 2: Comparison of 4-step SDXL distillation. Our 'Decoupled' method strictly follows the DMD2
training setting but employs our proposed decoupled-hybris (4) re-noising schedule. Indicators are evaluated on 10k COCO2014 val prompts.
Method
FID
CLIP-S 1
ImageReward
HPS V2.1 1.111
HPS V3
LCM (Luo et al., 2023a)
22.27
31.71
39.56
28.00
6.45
Turbo (Sauer al., 2024b)
27.27
32.16
46.09
29,83
9.09
Lightning (Lin al., 2024)
24.49
32.31
57.48
30.30
9.48
Flash (Chadehec ct al., 2025)
22.96
31.84
19.04
27.71
6.49
PCM (Wang ct al., 2024)
24.13
32.52
64.73
30.76
9.46
DMD2 (Yin et al., 2024a)
18.95
33.14
71.01
30,64
9.64
Decoupled (Ours)
17.80
33.62
78.61
30.34
9.79
where d-DMD is short for decoupled DMD. This modification allows us to decouple the renoising schedule of DM and CA, allowing principled experimental analysis. With this formulation, design an ablation study to evaluate four distinct schedule configurations for a 4-step generator:
Coupled-Shared: The original DMD approach where TCA 7DM, sampled from [0, 1].
Decoupled-Full. Both schedules are independent but cover the full range, TCA 7DM E [0, 1].
Decoupled-Conste Constrained: Both schedules are independent and constrained, TCA TDM > f.
Recoupled-Hybrid, The engine is constrained while the regularizer is not, TCA > t. 7DM E [0, 1].
The results, presented in Tab. for the Lumina-Image- evidence for our hypothesis. First, we confirm that merely decoupling the schedules while keeping them global @ yields negligible impact compared to the baseline ① demonstrating that the benefit comes from the schedule's range, not just its independence. More importantly, both configurations with constrained schedules (3 and @) significantly outperform the baselines across multiple bench- marks (Hu et al., 2024b; Wu et al., 2023; Ma et al., 2025). Crucially, our proposed Decoupled-Hybee setting ④ consistently achieves the best overall scores, validating our core proposal.
model (Qin et al., 2025), provide strong
The qualitative results in Fig. 5 offer further visual confirmation. Compared to the global schedule (@, top row), constraining the CA engine (3, middle row) introduces richer, finer details, confirming the benefit of focused engine. However, this configuration still suffers from color oversaturation, low-frequency artifact that its constrained DM regularizer fails correct. In stark contrast, our Gcoupped-HHbbre setting (4) bottom row) retains these enhanced details while effectively mitigating the saturation artifacts, yielding the most visually appealing and natural-looking images. These observations are decisively corroborated by comprehensive user study (Sec. D), where model @ achieved a unanimous 100% preference rate in model-level comparisons. 15 annotators consistently justified their choice by its ability to generate richer details, more realistic and less "greasy" appearance, and fewer structural deformities. Furthermore, a three-way way image-level ranking, model 4 was ranked first in 59.8% of cases, significantly outperforming the next-best model (3 at 33.8%).
Experiments on SDXL (Tab. 2) situate our findings within the broader landscape. For a rigorous comparison with DMD2 (Yin et al., 2024a), adopted their exact training configuration, including the GAN loss, and only replaced their re-noising schedule with our Decoupled-Hyy Hybbid approach. The results demonstrate a clear advantage, confirming the effectiveness of our proposed schedule.
Finally, to explore the full potential of our algorithm on top-tier models, we distilled a high- performance internal 6B model (Fig. 7). The resulting 4-step generator achieves performance largely on par with the original 80-NFE teacher (Tab. 6-15) at 95% NFE reduction. and exhibits superior fine details and texture compared the conventional DMD loss (0) shown in Fig. 6.
In summary, these results strongly validate that our engine-regularizer decomposition not only provides a deeper understanding but also unlocks tangible performance improvements, demonstrating the practical value of our new perspective.
5 CONCLUSION AND LIMITATIONS
In this work, we challenge the conventional understanding of DMD practice in complex tasks like text-to-image, revealing functional decoupling with CFG Augmentation (CA) the primary

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engine for few-step conversion and Distribution Matching (DM) the regularizer. This new perspective allowed us to observe the distinct properties each component and propose a principled improvement-a a decoupled re-noising schedule.
However, fundamental question remains unanswered: why does CA possess such a remarkable ability convert diffusion model into few-step generator? We find that providing precise answer is highly challenging, partly because the mechanism of CFG itself remains largely enigmatic. For interested readers, share our high-level, preliminary understanding and explanation of this issue in Sec. B. Nevertheless, we acknowlede ledge that significant gap remains towards rigorously accurate explanation, and we intend to explore this topic further in our future work.
ACKNOWLEDGMENT
This study was supported in part by the National Natural Science Foundation of China (No. 62206272). in part by National Key R&D Program of China Project 2022ZD0161 100, in part by the Centre for Perceptual and Interactive Intelligence, CUHK-led InnoCentre under the InnoHK initiative of the Innovation and Technology Commission of the Hong Kong Special Administrative Region Govermment, in part by NSFC-RGC Project N 4UHK498/24, and in part by Guangdong Basic and Applied Basic Research Foundation (No. 2023B151513000 XW).
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A DECLARATION ON THE USE OF AI TOOLS
In the research and writing process of this work, we utilized Large Language Models (LLMs) as an assistive tool. The application of LLMs was primarily limited two aspects: 1) For writing. we used LLMs to polish language, improve expression, and obtain suggestions regarding structure and flow. 2) For coding, LLMs were used to provide debugging assistance and to generate utility scripts, such as for data visualization. We hereby declare that the core ideas, novel methodology, experimental design, and main codebase this work were completed by the human authors. LLMs did not contribute these intellectual aspects.
B DISCUSSION: WHY DOES CA WORK?
In this section, we attempt to build a conceptual bridge to understand the efficacy CFG Augmenta- tion (CA) as the "engine" of ftw-step distillation. We do so by drawing parallel between diffusion models and Large Language Models (LLMs) under a unified view of sequential generation.
B. A PARALLEL PROBLEM: WHY CAN'T LLMS PERFORM N-TOKEN PREDICTION?
We begin by considering a parallel question in the domain of LLMs: why must they generate text token by token, rather than predicting the next N tokens simultaneously? Consider the prompt, "The richest person in the world is". Both "Elon Musk" and "Bill Gates" are plausible completions. A model cannot simultancously predict the first and second tokens, because the choice of the second token (e.g.. "Musk" or "Gates") is strictly conditional on the choice of the first ("Elon" or "Bill"), An attempt to predict both at once would risk generating incoherent combinations like "Elon Gates" or "Bill Musk", or more likely, averaged and meaningless representation.
The fundamental reason for this limitation that the model's role to predict a probability distribution for the next token, Ptokeen; pprompt). It cannot, however, control the outcome of the probabilistic sampling process that selects a single token from this distribution. This external, uncontrollable sampling event breaks the model's predictive flow. No matter how powerful the model, it cannot bypass this external intervention to predict tokeng, because any prediction makes could conflict with the yet-undetermined outcome of token1-
B.2 A GENERAL FRAMEWORK FOR SEQUENTIAL GENERATION
We can abstract this to higher level. Any sequential generator, at each step, faces three types of information:
Type 1 (Determined): Information that is already fixed and known (e.g., the input prompt).
Type 2 (Directly Determinable): Information for which the model can predict distribution of possibilities for the very next step.
Type (Directly Undeterminable): Information that can only be determined after some Type 2 information is resolved and becomes Type 1.
The process of sequential generation is the iterative conversion of information from Type 2 to Type 1, which in turn allows Type become Type 2. Importantly, we claim that the existence of Type information, whose resolution is contingent on an uncontrollable external decision on Type 2 information, the core reason for iterative generation.
B.3 FROM UNCONTROLLABL INTERVENTION TO DETERMINISTIC PATTERN
This analysis also points to a potential strategy for converting a sequential generator into a one-step generator: if the random, external decision-making process could be replaced with deterministic decision pattern, and this pattern could be "baked into" the generator itself. For Type information, what was previously random variable with non-zero entropy would become a determinable value. This would collapse the entire decision tree into a single, predictable path, allowing all information to be resolved in go.
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B.4 CONNECTING BACK TO DIFFUSION MODELS AND CFG AUGMENTATION
We posit that diffusion models are also sequential generators, which first establish low-frequency global composition (e.g.. the object is cat, dog) before adding high-frequency details (e.g.. the texture the fur). The relationship between composition and detail mirrors that of "Elon/Bill" and "Musk/Gates". We note that this viewpoint has been formally established Dieleman (2024).
Crucially, we argue that Classifier-Free Guidance (CFG) acts as an external intervention analo- gous to probabilistic sampling. While CFG deterministic bias, not stochastic process, is equally unpredictable from the model's perspective: The model is trained without awareness of CFG, and inference, canmot control the negative prompt or guidance scale (a) that will be applied. Furthermore, CFG, like sampling, transforms the model's prediction from averaged expectation into a specific, shifted value.
Our central hypothesis is this: CFG represents a specific, deterministic decision pattern. The CA term the DMD objective is the mechanism that "bakes" this decision pattern into the student generator's predictions. By doing it transforms the uncontrollable external force of CFG into an internalized, predictable behavior. The generation process, which was a tree of possibilities, collapses into a single, direct path.
Returning to our LLM example, what CFG Augmentation does is akin to telling the model: "Given the current input, the external process will always choose 'Elon' the first token. Therefore, you safely assume the first token is 'Elon' and directly predict 'Musk'." This is, we believe, the source of CA's power in enabling few-step image generation.
We acknowledge that the preceding discussion remains at the level of high-level ideas and that our hypothesis-that "CFG represents specific, deterministic decision pattern"-is strong assumption. We share this perspective here primarily to stimulate further investigation into this fundamental question and provide potential reference point for future work. We also intend conduct more in-depth study of this problem in our future research.
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C
PSEUDO-CODE
Algorithm Segginal&Deccuplee DMD Training Procedure
Require: Pre-trained teacher model Steat CFG scale a, number steps proxy weight
Ensure: Trained few-step generator Go
I: > Initialize student generator and fake model from the teacher
2: Go 8peal
3: Stkke Sreal
while converged do
5: P p- Generator Update Step
6: Sample generation step / from the few-step schedule {41.....AN] (xx)
7: Prepare generator input (e.g., via backward simulation for t f1)
Generate an image: Zgnn + (za)))
9:
"decoupled secoupled_schedule then D Decoupled DMD behavior-
10:
11:
Sample CFG augmentation noise level TCA ~ [tt,
12:
Sample Distribution Matching noise level TEM ~ 21(0, 1)
Re-noise the generated image for both schedules:
14:
Ercs < renoise [gen: TCA)
15:
Tru + renoise (Zgon. TDM)
16:
Withwith torch.no_ goo_grad)):
Calculate scores for the Distribution Matching (DM)
18:
Scund + Sreal (20Tm 7DM, text)
19:
Scund, DM Stike TOM, text)
20:
Calculate scores for the CFG Augmentation (CA) term
21:
sand, +- Steat (TeTs TCA text)
rel
22:
unesodd CA +- Sseal(Rrex) TCA, ")
23:
End With
24:
& Compute the two components of the update direction seal
25:
ADM f- Scund, DM
Scond, DM
fake
26:
ACa < (ax 1) rel
4 real
uncond, CA)
CA
27:
Apall ADM
ACa
28:
else
Original DMD behavior
30:
Sample single noise level r ~ (0,
31:
Re-noise the generated image: 3r f- renoiso T)
32:
Withwith torch.no_ggoooooeeeeo grad():
33:
Sand
Syeal (2Fr, T, text)
34:
Sunpood <- Sreal (IT,
real
35:
Sundd f
8aaaa T, textt)
36:
Sdig steal
(s
uuncood
37:
EndWith
38:
& Compute combined update direction
39:
Aona -- Setg
rell
tkke
40:
end if
41:
Update generator by minimizing the praxy loss
42:
Cpenxy + -IGo((z) stop_grad (oop_grad(Go(2) + x2
43:
Update Go by minimizing Leroxy
44:
45:
Fake Model Update Step
46:
This step be multiple times per generator update (TTUR)
47:
Sample a new noise level r' (((0, 1)
48:
Generate a new image with detached gradient: s'ga +- stop_ grad
49:
Re-noise the
image: 2i <- renoise(ziga.
50:
Lamoise || ( (I'r,,')) ='geal?
S1:
Update Stake using Lataniie
52:
end while
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D USER STUDY
To further validate the effectiveness of our proposed Gccopped-Hybbri schedule (4), we conducted comprehensive user study comparing the four few-step models from the ablation in Table 1. The study was divided into two parts: per-image ranking evaluation and per-model side-by-side comparison.
D.1 PER-IMAGE RANKING EVALUATION
In this part, compared the visual quality of models @ (Decoupled-Full), @ (Decoupled- Constrained), and @ Deccoupee-Hyybrine We randomly selected 500 prompts from the HPSv2 benchmark Wu al. (2023) and generated one image for each prompt using the three models. We then invited 10 professional annotators to perform forced ranking of the three images in each set based on their overall quality (e.g., a ranking of 2>3>1, with ties disallowed). To prevent positional bias, the order of the three images within each triplet was randomized, annotators could not determine which model generated which image based on its position.
The quantitative results are presented in Table 3 and Table 4. As shown, our proposed Decoupled- Hybrid schedule (0) demonstrates a significant and consistent advantage over the other configurations. It achieved first-place ranking in 59.8% % of the evaluations, far surpassing the 33.8% of the next-best model, @. The pairwise comparison in Table 4 further confirms this superiority, where model O achieved win rates of 60.6% and 83.4% against models @ and @, respectively.
Table 3:
Overall performance and rank distribution from the per-image user study. Our Decoupled- Hybrid schedule (0) ranked first in the majority of evaluations.
Model
Avg. Rank
1st Place (%) f
2nd Place (%)
3rd Place (%)
22) Decoupled-Full
2.748
6.4
12.4
81.2
( Decoupled-Connttranne
Constrained
1.692
33.8
63.2
3.0
Decoupled-Hyyrrt
1.560
59.8
24.4
15.8
Table 4: Pairwise win rates (%) from the per-image ranking evaluation. Each cell (row, col) shows percentage of times the model in the row was ranked higher than the model in the column.
x
Decoupled-Full
@ Decoupled-Coostrrined
Decoupled-
2 Decoupled-Fut Full
8.6
16.6
Decoupled-Consse Constrained
91.4
39.4
Decoupled- Recoupled-Hybrid
83.4
60.6
D.2 PER-MODEL SIDE-BY-SIDE COMPARISON
We further conducted per-model comparison gauge the overall preference between different schedules. In this setup, we performed three separate side-by-side comparisons: I (Coupled-Shared) vs. @ @ (Decoupled-Full) vs. @ and 3 DDecoppled-Constrainee randomly sampled 200 prompts from the HPSv2 benchmark (using a different random seed for each pair) and displayed the generated images to review all 200 image pairs and make single, model-level judgment which model (left or right) performed better overall. They were also asked to provide brief justification for their choice.
vs. @ For each comparison,
fixed two-column layout. We then asked 15 annotators
Table 5: Quantitative results from the per-model, side-by-side user study with 15 annotators. Our Recoupled-Hybrit model (0) achieved unanimous 100% preference rate all comparisons.
Comparison
# Prompts
Preference for Model @ (%)
② (Coupled-Shared) vs.
200
100% %
@ (Decoupled-Full) 4
200
100% %
C (Decoupled-Constee Constraiied)) vs.
200
100% %
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The quantitative results, summarized in Table 5, show a decisive victory for proposed Decoupled- Hybrid model (④). was unanimously preferred in all three head-to to-head comparisons, achieving a 100% win rate.
The justifications provided by the annotators shed light on the reasons for this strong preference. The most frequently cited advantages of our model (4) were its ability generate richer details, produce a more realistic/less over-saturated/not greasy texture/coloring, and exhibit fewer anatomical or structural deformities. The two-column comparison tables presented to the annotators for the per-model evaluation, along with the complete textual justifications from annotators, are included in the supplementary material zip file for reference.
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E DISTILLATION OF A HIGH-PERFORMANCE 6B INTERNAL MODEL
E.1 QUALITATIVE VISUALIZATION
To fully unleash the potential our algorithm and explore its performance on pethrpeeffrmance models, we also conduct experiments on an internal flow-matching www-naachiing-asedd based 6B model.
Fig. presents a qualitative comparison between our proposed decoupled- schedule (4) and the conventional DMD loss (@). Our method markedly leads to a pronounced improvement in the articulation of fine details and the authenticity of surface textures.
Fig. 7 showcases the performance of our distilled 4-step model, which demonstrates strong capabilities text rendering, artistic versatility, and photorealistic quality.
Figure 6: Qualitative comparison distilling internal 6B high regghpeerfomance model to step. For a pair of images, the left is generated by the model trained with conventional DMD loss, while the right is trained with our proposed decoupled hhybuleedhhybrid schedule
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Superior Bilingual Text Rendering
ORIGINAL MOTION PICTURE SOUNDTRACK
Decoupled DMD:
Call Me by your Name
CFG Augennation as the Spear, Distribution Matching the Shield,
Rethinking DMD:
L.D Engine
+ ReguuarrzarrMMM
RR
DMBS 2
L
stublityietdh
tiifics
t
CA-Engine
Reguvartoee
Our Beloved Gifts
Just Dropped
Acounti thi
Beautiful Thing
This Week's Hottes Vinyl Atmnmt Rock Euartha
90s
17 A 4 3000840
Artistic Versatility
Ultimate Realistic
Figure 7: Performance demonstration of our 4-step distilled internal 6B model
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E.2 QUANTITATIVE COMPARISON
Tab. 6 through Tab. 15 provide comprehensive quantitative comparisons of the model's performance on various benchmarks before and after distillation. The original 6B model requires 40 steps with CFG for inference, totaling 80 NFE (Number of Function Evaluations). After distillation with our decoupled-hybon schedule, the resulting 4-step model achieves performance that largely on par with the original teacher at 95% NFE reduction, with only minor fluctuations across different metrics.
Table 6: Summary of Quantitative Evaluation Results Across All Benchmarks.
Model
DPG Rench
GenEval
OneIG
THF--Bend
PRESM-Bench
CVTG-2K
LongTexteench
211
SDXL Podell al. (2023)
74.65
0.316
57.0
SD3 Medium Esser et al, (2024)
$4.08
0.63
67.46
66.09
66.1
FLUX. [Dey] Labs (2024)
83.84
0.06
0.434
71.09
71.78
08.5
0,8966
0.007
01003
Lumina image 2.0 Qin (2025)
87.20
0.73
0.353
0.334
Sa0.i Ciso (2025)
68.27
0.530
86.02
76.2
0.5924
0.86
0.878
Image [High] OpenAl (2012)
0.533
0.8569
0.619
Qwen-Image Wa (2025)
88.32
0.87
0.519
0.548
74.1
0.8388
0.941
0.966
Internal-68
88.
0.50
0.546
0.509
80.01
80.20
75.1
73.3
0.8604
0.922
0.945
Internal-68--unn
X8.53
0.78
0.544
11.33
82.15
78.94
75,3
75.3
0.8327
0.895
0.953
Difference
19
-0.002
40.002
-0.03
40.01
Table Quantitative Evaluation Results on DPG Bench Hu al. (2024a).
Model
Global
Eutity
Attribute
Relation
Other
Overall
SDXL Podell al. (2023)
83.27
82.43
80.91
86.76
80.41
74.65
SD3 MediumEiseer et (2024)
87.90
91.01
88.83
80.70
88.68
84.08
FLUX.I [Dev] Labs (2024)
74.35
90.00
88 96
90.87
88.33
83.
Lumina-Image Qin (2025)
91.97
94.85
87.20
Seedream3. u Gao et al. (2025)
94.31
92.65
91.36
92.78
88.24
88.27
GPT Image [High) OpenAl (2025)
88.89
88.94
92.63
90.96
85.15
Qwen-Image Wa et al. (2025)
91.32
91.56
92.02
94.31
92.73
88.32
Interal-6B
93.39
91.22
93.16
92.22
91.52
88.
Interal-6B-Turto
94.70
93.24
92.78
92.01
92.58
88.53
Table 8: Quantitative Evaluation Results on GenEval Ghosh et al. (2023).
Model
Single Object
Two Object
Counting
Colors
Position
Attribute Binding
Overall
SD3 Medium Esser et al. (2024)
0.98
0.74
0.63
0.67
0.34
0.36
0.62
FLUX.1 [Dev] (2024)
0.79
0.22
Lumina-Image 2.0 Qin ot (2025)
0.87
0.67
0.62
0.73
Seedream3.0 Gao et al. (2025)
0.99
0.96
0,93
0.47
0.80
0.84
GPT Image [High] OpenAl (2025)
0.99
0.92
0.85
0.92
0.75
0.61
0.84
Qwen-Image We (2025)
0.99
0.92
0.89
0.88
0.76
0.77
0.87
Internal-6B
1.00
0.94
0.70
0.90
0.51
0.72
0.80
Internal-6B-I1
0.88
0.55
0.72
Table 9: Quantitative Evaluation Results on OneIG-EN Chang et al. (2025).
Model
Alignment
Text
Reasoning
Style
Diversity
Overall
SDXL Podell ct. (2023)
0.688
0.029
0.237
0.332
0.296
0.316
FLUX.1 [Dev] Labs (2024)
0.786
0.523
0.253
0.368
0.238
0.434
Lumina Image 2.0 Qin et (2025)
0,819
0.106
0.270
0.354
0.216
0.353
Seedream3.0 0 Gao al. (2025)
0.818
0.865
0.275
0.413
0.277
0.530
GPT Image [[ligh] OpenAl (2025)
0.851
0.533
Qwen-Image Wu et al. (2025)
0.882
0.891
0.306
0.418
0.197
0.539
Internal-6B
0,881
0.987
0.280
0.387
0.194
0.546
Internal-6R- Tu-Turbo
0.876
0.972
0.283
0.404
0.186
0.544
21

---

Published as a conference paper at ICLR 2026
Table 10: Quantitative Evaluation Results on OnelG-ZH Chang al. (2025).
Model
Alignment
Text
Reasoning
Style
Diversity
Overall
Lumina-Image 2.0 Qin al. (2025)
0.731
0.136
0.221
0.343
0.240
0.334
Seedream3.0 Gao al. (2025)
0.793
0.928
0.281
0.397
0.243
0.528
GPT Image [High]] OpenAl (2025)
0.812
0,650
0.300
0.449
0.159
0.474
Qwen-Image Wi et al. (2025)
0.825
0.963
0.267
0.405
0.279
0.548
Internal-6B
0.829
0.990
0.209
0.377
0.179
0.529
Internal-6B- -TrTbo
0.831
0.986
0.272
0.388
0.175
0.531
Table 11: Quantitative Evaluation Results on TIlF-Bench Wei et al. (2025).
2018
00:00
81:31
11
3033
61.0
4112
40.19
M55A
4777
4003
41.00
13.5
19.93
11.00
65.00
Use
uge Logg (opeerictts
50:10
36.00
6831
01:22
11.00
1832
1979
5-12
7131
5.0
31.00
7337
1860
185.0
0215
18.11
86
11.0
Table 12: Quantitative Evaluation Results on PRISM-Bench-EN Fang et al. (2025).
Padky
Afferiss
Campeslke
Long lext
Hade
Don
Dey
Al.
Aeg
24
Am
Are
Ame
Km
Arg
All
Aec
Deg
Km
Are.
Ama
20g
21.4
78.
12.2
13.8
485
63.1
33.3
AttiMMeiee foon
GED41
35.6
568
56.5
54.
03.1
61.2
11.2
17.0
42.1
23.
3.6
856
2355
983
140
66.1
beckmand Dhevedl
16.
81.
163
175
213
743
884
631
842
18.
123
633
935
151
38.3
383
764
96.
K31
12.
76.
15.5
17.8
065
162
445
120
214
645
664
655
88
26-1
661
639
965
363
16.
764
135
830
68.
161
129
375
363
104
764
118
25.
145
P11
115
15.5
06.
193
565
111
968
180
71.1
794
750
153
3422
153
Table 13: Quantitative Evaluation Results on PRISM-Bench- ZH Fang et al. (2025).
Oreall
S (302))
26.
788 713
71.4
913
15.1 939
113 00
(Rul (3255
17.5
K24 652
718
18a
953
369
078
113
443
7/9
815
18.3
11.
M6.
185
166
M1
764
245
152
851
815
181
23
261
911
17x
519
074
661
119
111
Table 14: Quantitative Evaluation Results CVTG-2K Du et al. (2025).
Word Accuracy
Model
NED
CLIPScore
regions
regions
4 regions
5 regions
average
FLUX.1 [Dev] Labs (2024)
0.6089
0.5531
0.4661
0.4316
0.4965
0.6879
0.7401
Seedream3.0 Gao al. (2025)
0.6282
0.5962
0.6043
0.5610
0.5924
0.8537
0.7821
GPT Image [High] OpenAl (2025)
0.8779
0,8659
0,8731
0.8218
0.8569
0,9478
0.7982
Qwen-Image et al. (2025)
0.8370
0,8364
0.8313
0.8158
0.8288
0.9116
0,8017
Internal-6B
0.8652
0.8736
0. 0,8664
0.8404
0.8644
0,9419
0.8107
Internal-6B- Gu-Torbo
0.8417
0,8457
0.8350
0.8148
0.8327
0.9287
0.8411
Table 15: Quantitative Evaluation Results LongText-Benne Bench Geng et al. (2025).
Model
LongText-Bench-EE
LongText-Bench-
FLUX.1 [Dev] Labs (2024)
0.607
0.005
Seedream3.0 Gao et al (2025)
0.896
0.878
GPT Image [High] OpenAl (2025)
0.956
0.619
Qwen-Image We et al. (2025)
0.943
0.946
Internal-6B
0.922
0.945
Internal-6f. -ur-bo
0.895
0.953
22

---

Published as a conference paper at ICLR 2026
F ADDITIONAL EXPERIMENTAL RESULTS
F.1 DETAILED RESULTS OF RE-NOISING SCHEDULE ABLATION
In Tab. of the main text, we have already presented the overall performance comparison for different re-noising schedule configurations. In Tab. 16 and Tab. 17, we additionally provide the fine-grained results on the HPS v2.1 and HPS v3 benchmarks, respectively.
Table 16: Detailed results of the Tab. experiment on the HPS v2.1 benchmark.
Method
Concept-Art
Photo
Anime
Paintings
Average
Original (50 steps)
30.35
28.24
31.74
30.47
30.20
Ørca ToM [0, 1] (DMD)
30.31
29.95
31.72
30.45
30.61
ØrCa E [0, 1], TDM [0,1]
30.31
30.25
31.85
30.34
30.69
@rCA > f, 7DM > f
31.48
30.87
32.98
31.51
31.71
@TCa f, TDM E [0,
32.37
30.87
33.61
32.31
32.29
Table 17: Detailed results of the Tab. experiment the HPS v3 benchmark.
Method
Animals
Architecture
Arts
Characters
Design
Food
Original (50 steps)
9.562
10.418
9.292
10.822
8.358
10.160
① 7DM E [0, (DMD)
10.377
11,537
9.077
11.061
8.112
11.520
2 [0, 1], 7MM E [0, 1]
10.338
11.539
8.929
11.101
8,059
11.572
TCA TDM
11.309
12.388
9,690
11.975
8.694
12.096
TCA t, Tom E [0.
11.873
12,899
10.351
12.562
9.308
12.425
Method
Nat. Soe.
Others
Plants
Products
Science
Transportation
Original (50 steps)
9.781
9.623
9.881
9.409
8.477
9.659
TCA 7bM E [0, (DMD)
10.138
10.797
10.528
10.994
8,417
11.503
TCa E 00, 11. TbM E [0,
10.046
10.787
10.600
11.049
8,358
11.484
TCA t, 7рм t
11.177
11,553
11.390
11.508
8,905
12.256
TDm
00, 1]
11.592
12.138
11.846
11.841
9.451
12.782
23

---

Published as a conference paper at ICLR 2026
F.2 QUALITATIVE COMPARISON OF DIFFERENT REGULARIZERS
In Fig. of the main text, we have already traced the quantitative indicators of combining the CFG Augmentation (CA) with different regularizers. In Fig. 8, we additionally provide visualization of the generated samples from this experiment.
No Regression
Mean-Va Var Regression
Distribution Matching
GAN
600 Steps
Steps
2000 Steps
PLAT FLAT
ACRAT FRE
NV
TVISS
TITM
4000 Steps
TV
8000 Steps
Figure 8: Sample visualization on combining training CA with different regularizers (Fig.
24


Reviews:
[{"review_id": "2917QO8ycq", "reviewer": "Reviewer_vHFL", "summary": "The paper investigates the respective roles of the two loss components—CFG augmentation and distribution matching—in the DMD framework. Through carefully controlled experiments, the authors conclude that CFG augmentation serves as the primary driver for few-step or one-step conversion, while distribution matching acts mainly as a regularizer. They further argue that, although alternative regularizers could be used, distribution matching remains the best fit. Finally, the paper observes that assigning different $\\tau$ values to the two loss terms yields additional performance improvements.", "questions": "See weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "* Provides a timely and insightful analysis of the functional roles of DMD’s two loss terms, addressing the open question of why DMD excels in few-step or one-step generation.\n* The authors design careful and hypothesis-driven experiments to isolate and test the contribution of each loss term, leading to well-supported conclusions. \n* Based on these insights, the paper proposes using distinct $\\tau$ values for the two terms, leading to measurable performance gains.", "weaknesses": "Most experiments rely primarily on qualitative evaluation (visual inspection of generated images). While visualization is valuable for illustrating effects, heavy reliance on qualitative judgments risks confirmation bias—highlighting supportive examples while overlooking contradictory ones. A more scientifically rigorous approach would involve defining quantitative metrics and validating observations across the entire test set, to ensure statistical robustness and reproducibility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zQW7R2L7fz", "reviewer": "Reviewer_uRhT", "summary": "This paper challenges the conventional understanding of the underlying mechanisms of Distribution Matching Distillation (DMD) for distilling pre-trained diffusion models into one/few-step student models. While it might be tempting to think that DMD's success mainly stems from matching the student's output distribution to the teacher's output distribution, the authors decompose the DMD loss into a distribution matching (DM) term and a CFG augmentation (CA) term, arguing that it is the CA term that plays the primary role in the distillation process. Surprisingly, the DM term functions more like a stabilizing regularizer and could be replaced by other regularization terms with different trade-offs. Leveraging this insight, a decoupled noise schedule is proposed for CA and DM to improve the model performance.", "questions": "Could the authors comment on the issue in the weakness section? One way to address this issue is to reduce the claim to \"the CA term is the engine for DMD **in conditional generation**\".", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper identifies a discrepancy between theory and practice in DMD that CFG is only used in the teacher model but not the student model. This is an interesting observation and a natural motivation for this important research topic.\n2. The decomposition of the DMD loss into the DM and CA terms provide novel and valuable insights towards a better and principled understanding of the underlying mechanism of DMD.\n3. The arguments and hypotheses in the paper are supported by extensive experiments with ablation studies, demonstrating impressive empirical results.\n4. The paper is well-written and easy to understand. It also acknowledges the limitations of the current understanding of the CA term and provides some preliminary discussions.", "weaknesses": "Overall, I like the paper very much. My only concern is the paper's claim about the CA term being the engine for DMD, which is a bit strong to me. For example, early DMD papers achieved great distillation performance on unconditional generation for CIFAR images, which is not discussed or explored in this paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tp2YnkYobh", "reviewer": "Reviewer_rsWL", "summary": "This work revisits what makes DMD effective. While DMD’s success is usually credited to matching the student’s output distribution with a teacher model, the authors show that the true driver is an overlooked component called CFG Augmentation (CA). They find that CA acts as the core engine of distillation, while the Distribution Matching (DM) term mainly serves as a stabilising regularizer. They also show that recognising this separation enables a clearer understanding of DMD and allows improvements such as decoupling noise schedules for better performance.", "questions": "See above, why the unconditional CIFAR works with only DM term?\n\nHappy to increase the score if the concern could be solved.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "I really like this research topic and believe the distribution-matching distillation is an under-explored topic, and only from a divergence perspective, it can't answer why it works or why it doesn't work in some scenarios, so I think the topic of this paper is very valuable.\n\nThe experiments are also sound, which can support the argument.", "weaknesses": "My major concern with this paper is that I found the conclusion a little bit conclusive.\n\nThe argument is CFG Augmentation is the engine for dilatation, and Distribution Matching is the regularizer for stability.  \n\nHowever, many CIFAR experiments don't use label-conditioned and can achieve one-step distillation, e.g. the original diff-intruct paper or more recent paper: https://arxiv.org/pdf/2502.08005. In this case, the pure driven engine is only the distribution matching term, which couldn't be explained by the hypotheses introduced in the paper.\n\nIt may be possible that CFG can play a key role in the conditional generation, but it is hard to say DM is not the engine.\n\nMinor: The distillation also relates to the student model score estimation quality, initialisation, teacher model's score quality, etc... It would be good to add some analysis on that.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)