Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling
Authors: Kyungmin Lee
Sihyun Yu
Jinwoo Shin
Venue: ICLR 2026 Poster (2026)
Keywords: Few-step diffusion
Diffusion models
Flow-based models
generative models
diffusion transformer
Primary area: generative models

Abstract: Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce \emph{Decoupled MeanFlow}, a simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1–4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256$\times$256 and 512$\times$512, our models attain 1-step FID of 2.16 and 2.12, respectively, surpassing prior art by a large margin. Furthermore, we achieve FID of 1.51 and 1.68 when increasing the steps to 4, which nearly matches the performance of flow models while delivering over 100$\times$ faster inference.

Published as a conference paper at ICLR 2026
DECOUPLED MEANFLOW: TURNING FLOW MODELS INTO FLOW MAPS FOR ACCELERATED SAMPLING
Kyungmin Lee Sihyun Yu KAIST
Jinwoo Shin
ABSTRACT
Denoising generative models, such diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization emror. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce Decoupled MeanFlow, simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1-4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256x 256 and 512 512, our models attain 1-step FID of 2. 16 and achieve
2.12, respectively, surpassing prior by a large margin. Furthermore, FID of 1.51 and 1.68 when increasing the steps to 4, which nearly matches the performance of flow models while delivering over 100x faster inference.
Velocity
Average Velocity
3.25
DMF-XU/2 (ours)
SIT-XL/Z+REPA
DIT/SIT Block
DIT/SIT Block
3.00
DIT/SIT Block
DIT/SIT Block
2.50
Timestop
DIT/SIT Block
DIT/SIT Block
2.00
DIT/SIT Block
DIT/SIT Block
DIT/SIT Block
DIT/SIT Block
1.50
Current
Currett
2
4
109
434
Timesteo
NFE
Accelerating diffusion transformer via Decoupled MeanFlow. (Left) Our model, Decoupled MeanFlow (DMF), converts a flow model into flow map by decoding the intermediate representation with next timestep while preserving the original architecture. (Right) Fine-tuning DMF-XL/2 to predict average velocity (Geng al., 2025a) significantly accelerates the sampling speed of flow model RST::XL+REPA; Yu et al. 2025), while maintaining the performance.
Figure 1:
INTRODUCTION
Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2021) and flow mod- els (Lipman et al., 2023; Albergo et al., 2023) have emerged as effective and scalable approaches for generating high-quality visual data, including images (Ramesh et al., 2021; Saharia al., 2022; Rombach et al., 2022; Esser et al., 2024) and videos (Blattmann et al., 2023; Brooks et al., 2024;
Polyak et al., 2024; Wan et al., 2025). Despite their success, improving sampling efficiency remains key challenge, since producing high-quality samples typically requires many denoising iterations.
Model weights and code available at https:://// thub. com wtt.c/cm/////// /ywngmnunnggnnnm ee//mmf

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Published as a conference paper at ICLR 2026
Figure Qualitative examples. Selected samples from our DMF-XL/2+ models trained on ImageNet 512x512 (top row) and ImageNet x (bottom row) using NFE (left), 2 (middle), 4 (right).
To address this inefficiency, recent research has explored principled methods for designing diffusion models with fewer sampling steps. Consistency models (Song et al., 2023; Song & Dhariwal, 2024; Lu Song, 2025; Geng et al., 2025b; Peng al., 2025; Heek et al., 2024) enforce consistency between the denoised outputs from adjacent timesteps, enabling 1- or 2-step generation. While promising, these models struggle scale effectively beyond two steps (Sabour et al., 2025). Another line of work focuses on learning flow maps, which models the average velocity between two timesteps (Kim et al., 2024; Geng et al., 2025a; Sabour et al., 2025; Boffi et al., 2024; 2025). In particular, MeanFlow (Geng et al., 2025a) provides principled generalization of flow matching, showing that flow maps can achieve performance comparable to standard flow models.
While MeanFlow demonstrates the potential of flow maps, its architectural design remains under- explored. Specifically, integrates the next timestep information throughout the diffusion trans- former (Peebles & Xie, 2023), implicitly assuming that both encoder and decoder must rely on Yet, this assumption may be unnecessary: the encoder's role is to extract a representation from noisy inputs, where incorporating future timestep information may add little value. In contrast, the decoder is precisely where the next timestep should matter, as it governs how the model predicts future states.
In this paper, we introduce Decoupled MeanFlow (DMF), simple approach that transforms pretrained flow models into flow maps without altering their architecture. Our key idea is to decouple the diffusion transformer into encoder and decoder components: the encoder processes the current timestep, while the decoder incorporates the next timestep (see Fig. 1). This formulation avoids unnecessary architectural modifications while retaining compatibility with existing flow models.
Our design is inspired by recent works to rethink the representational structure of generative models, such as representation alignment (Yu et al., 2025), regularization (Wang & He, 2025), and masked modeling (Li et al., 2024). We hypothesize that the next timestep information is irrelevant during representation encoding and only necessary decoding for learning flow maps.
Our approach offers several advantages. DMF can fully reuse the pretrained flow model without architectural modification. As a result, any flow model can be seamlessly repurposed as a flow map model. We show that even without fine-tuning, the converted models produce high-qualit samples, often surpassing their original flow model counterparts (Fig. 3b). Moreover, fine-tuning only the decoder substantially accelerates sampling while preserving quality (Fig. 3c).
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Beyond the method itself, provide comprehensive analysis of Decoupled MeanFlow. We show that fine-tuning from pretrained flow models not only yields higher performance than training flow maps from scratch, but also requires fewer training compute, making our approach more efficient (Fig. 4). Moreover, our study reveals that the representational capacity plays a critical role in learning effective flow maps, highlighting the importance of encoder-decoder decoupling (Tab. 1 and Tab. 2).
Quantitatively, Decoupled MeanFlow sets a new state-of-the-art in few-step generative modeling. On ImageNet x56, our model achieves I-NFE FID=2.16, surpassing prior few-step diffusion models (Geng et al., 2025a; Frans et al., 2025; Zhou et al., 2025) and other approaches such as GANs (Sauer et al., 2022) and normalizing flows (Gu et al., 2025). When increasing the number of steps to 4, DMF reaches an FID=1.51, matching the performance of flow models (Yu et al., 2025) that require over 100x more computation during inference (see Tab. 3). Our approach successfully applies to higher resolution, for example, on ImageNet 512 1522, we achieve 1-NFE FID=2.12 12, and 2-NFE FID=1.75, outperforming the prior art sCD (Lu & Song, 2025) (see Tab. 4).
PRELIMINARIES
Flow models. Flow models (Lipman et al., 2023; Albergo et al., 2023) (or diffusion models (Ho et al., 2020; Song et al., 2021)) consist of forward process that adds noise to the data, and reverse process that gradually denoise noisy input to clean data. Formally, given a data Xy ~ Pdata and noise ~ ~N I), the forward process at time E [0, 1] is given by x; axXo + dec, where a and or are coefficients that satisfy (nn = σi = and on an = O. Training a flow model vo is done by
predicting the veloeity txx,t) R + ofe| x x.] with flow matching objective as follows:
(G) = Ex..t (x,, t) - v(x, )
(1)
Given the velocity (x(x, 1), the generative reverse process obtains a sample by solving the probability flow ODE for x,, i.e. dx, = vo(x,, ()d/. Note that the exact solution of ODE for x, from time t to is given x, x, + J,"
r)dr. In practice, since the integration is intractable, we resort to numerical methods, e.g., Euler's method, where the solution x, from X; is given by (r- ()x,))v(xx.d t). However, such numerical approaches require a large number of denoising steps or high-order methods (Karras et al., 2022; Lu et al., 2022; 2025) to achieve high-quality samples in order to reduce the time-discreiization error.
x,
Flow maps To accelerate the sampling, recent works (Geng et al., 2025a; Sabour et al., 2025; Boffi al., 2024) propose to learn a flow map between two timesteps that accelerate the inference speed via reducing the discretization error. Let (x,, t, r) be a flow map of x, from to and the ODE solver with flow map model be x, = x; + (r ( r). Then the dime-iiscettization error of the flow map ODE solver can be written as following:
Err (x,( r) = [. v(x, v(xx,))dr> - (r-t)upff (r-)))dd(rttuuuuuuuu (t)))
One can derive the training objective for the flow map model by minimizing the uime-disretiizatinn еттоr Eq. (2), Specifically, since the integration is achievabe,,,, MeanFlow (Geng et al., 2025a) introduced a training objective that minimizes the gradient norm of discretization error:
LMF = Ex,r (x (,r) v(x., (r) at uo( L, b.) |7
where the last term is computed by Jacobian-vector product (JVP) between primal vectors (0aus, Oo 0,) and tangent vectors (v, 1, 0) using following identity:
d uo(x,, t,r) dx, Oug dus
Oug 0x: Ōt
due
+
= vxx,,t)
dt
dt 0x Ōt
In practice, to eliminate the double backpropagation for JVP and case the optimization (Lu & Song, 2025; Frans et al., 2025; Geng et al., 2025b), we set Ugg = v + (r t) ar and optimize with (f)(()) = Ex.rlllu, u (ugg 11 where sg is a stop too-grrdieet operator. Remark that minimizing Eq. (3) alone cannot make the discretization error to be zero, as it only optimizes the gradient norm to be zero (i.e., first-order condition). Thus, it requires to satisfy boundary condition (i.e. r = t), which becomes equivalent to flow matching objective as in Eq. (1).
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Designing flow map architecture. To encode the timestep into the diffusion model, it is common practice to use positional embedding layer (Ho et al., 2020; Vaswani et al., 2017) that conditions throughout the layers. For instance, Diffusion Transformer (DiT; Peebles & Xie 2023) uses timestep embeddings to modulate the outputs of MLP and attention layers inside the transformer blocks. To implement flow maps, recent approaches (Zhou al., 2025; Geng et al., 2025a; Sabour al., 2025) use an extra timestep embedding layer for r and add the embeddings from and r (or t r) for the condition embedding (see Appendix B.1 for visualization).
Model Guidance. Classifier-free guidance (CFG; Ho & Salimans 2022) is a common practice to enhance conditional generation, where it interpolates between conditional and unconditional velocities control. However, CFG comes at the cost of doubling the inference compute. To reduce the inference cost, model guidance (MG; Tang et al. 2025) adjusts a target velocity as following:
v'e t, y) v(xe, t) + w (vo((x,, y, v)(x,,)),
where y is a condition and w E (0, 1) is a model guidance scale. Then, training with MG is done by applying stop-gradient operator to Vigi and replace v with vl in Eq. (1). Notably, MG is effective when training flow map, which enables high-quality 1-NFE generation (Geng et al., 2025a). We further provide details of model guidance in Appendix E.
PROPOSED METHOD
3.1 DECOUPLED MEANFLOW
Previous works have shown that diffusion and flow models implicitly perform representation learn- ing (Li et al., 2023; Xiang et al., 2023; Chen al., 2024), and improving the representations further enhances the generation capability (Yu et al., 2025; Wang et al., 2025; Wang & He, 2025). As such, one can reinterpret flow model vx(x, t) as the composition of an encoder fo : X' [0, 1] - 7 and decoder go H x [0, 1] + X' such that
go o fe. where h, fo(x,, () and va (Xx, () = go (h., ().
From this perspective, the representation encoded by So should also matter learning high-quality flow map. However, the architectural design of flow maps remains unclear. Previous works (Kim et al., 2024; Zhou et al., 2025; Geng et al., 2025a) follow a straightforward approach that the next timestep is provided to both the encoder and the decoder. Yet, this design may introduce redundancy: the encoder's 's task is to extract semantic features from Xs, for which the next timestep r may be irrelevant. Conversely, once the encoder produces h,, the decoder's role is to predict the average velocity toward timestep r, which may no longer require the original t.
These observations motivate us to decouple timestep conditioning in the encoder and decoder. Specifically, we propose to drop r from the encoder and from the decoder, leading to the formulation (x(x,,t,r) r) go (fo (x,, r). We refer to this architectural design as Decoupled MeanFlow (DMF), as the encoder and decoder are conditioned on different timesteps in a complementary manner. Following Yu et al. (2025), we partition the diffusion transformer into the first d layers as encoder fe and the remaining é - d layers as decoder ga, where l is the total number of blocks. To avoid introducing additional parameters, we reuse the same timestep embedding layer for both & and r, preserving the velocity prediction module of the original flow model (see Fig. 1).
Your flow model is secretly a flow map. This formulation suggests that any pretrained flow model can be converted into flow map via DMF. To test this hypothesis, we take the SiT-XI/2+REPA (Yu et al., 2025) pretrained on ImageNet (Deng et al., 2009), convert it into a flow map (DMF-XL//) without any fine-tuning, and compare their generative performance. We generate 50K samples using the Euler solver without classifier-free guidance (CFG) and evaluate FID (Heusel et al., 2017).
In Fig. 3a, we vary the encoder depth d for DMF with 16 denoising steps. Interestingly, DMF consistently improves as the decoder becomes smaller, and even outperforms the original SiT model in several settings. In Fig. 3b, fixing d=22, DMF maintains a clear advantage across denoising steps from 16 to 128. These results confirm that flow models can be transformed into flow maps without any tun-tunnng, and that carefully choosing the quality. We further investigate this finding across different flow models (see Appendix F).
decoder split can even yield better generative
Representation matters for flow map. We next study how encoder representations influence flow map quality. To this end, we freeze the encoder (d=22) and fine-tune only the decoder (and timestep
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DMF SIT-XL/2-REPA
DMF (Decader FT)
25.0
SIT-XL2-REPA
30
22.5
FID-50K
FID-50K
RD- 10-S0K
25
20.0
SIT-XL/--RPPA
11
20
17.5
16.0
12.5
10.0
16
Depth
Denoising Steps
Denoising stops
(a) Varying depth
(b) DMF vs. SiT
(c) Decoder-only fine-tuning
Figure 3: Pretrained flow model as a flow map. Comparison between pretrained flow model (SiT- XL/2+REPA; Yu et al. 2025) and converted flow map (i.e., see Fig. 1) with FID-5OK is reported. (a) Converted DMF without fine-tuning (DMF w/o FT) outperforms SiT-XL+REPA when chosen proper decoder depth. (b) Fixing depth to 22 and varying the denoising steps, DMF w/o FT consistently outperform pretrained SiT-XL/2+REPA, (c) By freezing the encoder and fine-tuning the decoder with flow map loss with guidance, recoder-tuned DMF (DMF Decoder FT) achieves substantial gain in sampling efficiency compared to SiT-XL/2+REPA with CFG.
embeddings layers) using the flow map training objective Eq. (3) with model guidance. We fine-tune SiT-XL/2+REPA for 40 epochs on ImageNet 256 resolution.
As shown in Fig. 3c, the decoder fine-tuned DMF achieves substantial efficiency gains: with only 8 denoising steps, it reaches FID=1.76, outperforming the baseline SiT-XL/2+REPA with CFG scale 1.5. This demonstrates that high-quality encoder representations learned by flow models can be effectively transferred to flow maps through DMF. However, we also observe that the 1-step performance remains limited when the encoder is frozen, indicating that the encoder must be jointly optimized to unlock the full potential of 1-step generative modeling.
3.2 IMPLEMENTATION
Training algorithm. Since our method combines the flow matching (FM) loss Eq. (1) with the McanFlow (MF) loss Eq. (3), sample two independent sets of noise and timesteps: (EFM, fPM) for FM loss, and (CME, bar. TMF) for MF loss. For each data sample Xy ~ Pdatu- we compute the total loss as the sum of FM and MF losses.? 2 We remark that while reusing the same (c, for both FM and MF objectives is possible, it often destabilizes training. The procedure is summarized in Algorithm 1.
Flow matching warm-up. Training flow maps is typically more expensive than training flow models due to additional forward passes. For example, computing the MF loss requires Jacobian-vector product (JVP) computations, which can cause memory issues if attention operations are not carefully optimized (Lu & Song, 2025). The cost further increases when model guidance is applied, since guidance-aware targets must be computed.
To mitigate this, we adopt two-stage strategy: first train a flow model with FM loss, then convert it into DMF and fine-tune with MF loss added. We find that pretrained flow models adapt rapidly to flow maps, especially when their representations with representation alignment (Yu et al., 2025) converge faster (see Tab. 1). As a result, our strategy achieves significantly better scaling than training a flow map from scratch (see Fig. 4).
strong, e.g., models trained longer enhanced
Adaptive weighted Cauchy loss. In practice, the MF loss exhibits high variance, which can hinder stable training. Prior works (Song & Dhariwal, 2024; Geng et al., 2025b; Lu Song, 2025; Geng et al., 2025a) introduce robust losses to address this. Inspired by these, we employ the Cauchy (Lorentzian) loss (Black & Anandan, 1996; Barron, 2019), defined as
Caaudhy (0) = log (O))(() +c)
(5)
where e >> 0 is a constant. Like Huber (Song & Dhariwal, 2024) and E losses (Geng et al., 2025b), the Cauchy loss behaves linearly near zero but suppresses the effect of large outliers.
To further improve stability, we follow Karras et al. (2024b) and incorporate adaptive weighting by modeling the residual error distribution of the MSE as Cauchy for each (t,r) pair. This yields the
In contrast, Geng al. (2025h) splits hatch into two groups (e.g., 75% for FM and 25% for MF).
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10
From Scratch
Figure 4: Effect of Flow Matching warmup. We plot 1-step FID for DMF-L/2 trained from scratch, DMF-L/2 fine-tuned from SiT-L/2 400K and 800K pretrained models. We plot total train- ing compute used for training. We see that fine-tuned model quickly recovers 1-step per- formance, and DMF-1/2 fine-tuned from 800K SiT-L/2 model achieves better performance than others, while using fewer total training flops.
FM warmup 400K
1-step FID (NFE =
FM warmup
3x10 Training Compute (FLOPs, log scale)
2x
adaptive weighted Cauchy loss (see Appendix A.1 for derivation):
LDMI-(B (0) Exs,r log e ((t,r) [x( (xce, -r -r dup
o(t, (6)
dt +1 2
where Φ : [0, x [0, + R is weighting function. The same formulation is used for FM loss.
Time proposal. Sampling timesteps from a logit-normal distribution has proven effective for training flow models (Karras al., 2022; Esser et al., 2024). For flow maps, however, we require (1,r) pairs with / >> r. Thus, we follow Geng et al. (2025b) to sampler (4,r) by drawing two logit-normal samples and taking their maximum and minimum.
Notably, as shown in Fig. 3, DMF models converted from flow models already predict accurate average velocities when close For I-step generation, it is therefore beneficial to sample pairs where f and r are far apart, particularly with r close to zero. To encourage this, we modify the proposal distribution accordingly, which accelerates 1-step generative modeling (see Appendix A.2).
Samplers. Note that the generation for DMF model can be done by Euler's method, i.e., x, X; + (r - t) (xt, t, r). Alternatively, as the model becomes capable of 1 1-step sampling, we also consider restart sampler (i.e., used in consistency models (Song et al., 2023)), which predicts &g. and diffuses into x,. Formally, the algorithm of restart sampler can be written as follows:
tuo (u, 1, 0),
X, + 0, a where e'~N (0,1)
Note that restart sampler is as performative as Euler sampler, and we observe trade-offs between them when evaluated with different metrics, e.g., see Fig. 5. We also examine stochastic samplers that interplays between Euler and restart sampler (Kim et al., 2024) in Appendix C.
4 EXPERIMENTS
Dataset and model. We conduct our experiments on ImageNet (Deng et al., 2009) dataset following ADM (Dhariwal Nichol, 2021) preprocessing protocols. We use latent Diffusion Transformer Peelees & Xie 2023) as our backbone, where we perform generative modeling on the latent space using pretrained VAE (Rombach al., 2022). To train flow models, we follow SiT (Ma et al., 2024) and REPA (Yu et al., 2025) when using representation alignment. See Appendix B for details.
Implementation. For each experiment, we use BF16 mixed- mixed-precision to prevent overflow, and Flash-Attention (Dao, 2024; Shah al., 2024) save GPU memory and accelerate training. Similar to (Lu & Song, 2025), we use customize the Flash-Attention kernel to support JVP computation.
Evaluation. We evaluate the 1-step (NFE 1) and 2-step (NFE = 2) generation with Euler solver by default. For comparison, we use Fréchet Inception Distance (FID; Heusel et al. 2017), Inception score (IS; Salimans et al. 2016), and Fréchet Distance with DINOv2-I/14 (Oquab et al., 2023) (FDpinov2; Stein et al. 2023) evaluated on 50K samples. See Appendix D for details.
4.1 ABLATION STUDY
We validate the effectiveness of DMF and study the effect each component through experiments. Specifically, we aim answer the following questions:

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Table 1: Ablation study. All models are fine-tuned from flow model (SiT-L/2) trained for 400K iterations. Depth denotes the number of encoder layers for DMF models, where total number of layers is 24. MG denotes the usage of model guidance (MG) during fine-tuning, and REPA denotes usage of representation alignment during flow model training. We report 1-step (NFE = 1) and 2-step (NFE = 2) FID, IS, FD for each MF-L/2 and DMF-L/2 model. We denote + and f to indicate whether lower or higher values are better, respectively.
1-step (NFF = 1)
2-step (NFE = 2)
Method
Depth
MG
REPA
FID 4
IS
FDDnNww2 4
FID 4
IS f
FDDNNOw2 +
MF-L/2
X
20.6
72.7
540.1
18.1
77.6
476.3
DMF-L/2
12
X
21.9
69.3
545.1
17.9
79.2
477.9
DMF-L/2
16
X
20.1
75.0
531.5
17.6
80.4
470.5
DMF-L/2
18
X
19.3
79.0
531.6
17.3
81.4
461.1
DMF-L/2
20
X
19.5
79.2
541.4
17.4
81.1
462.8
MF-L2
V
5.27
185.1
291.2
4.09
214.9
215.7
DMF-L/2
18
V
4.53
197.8
275.6
3.58
225.3
197.4
MF-L/2
x
15.8
90.5
421.7
12.6
102.7
361.2
DMF-1/2
18
X
14.2
99.7
419.9
11.8
105.6
340.2
MF-L/2
3.65
219.8
205.2
2.63
257.3
136.8
DMF-L/2
18
3.10
229.8
199.7
2.51
264.6
127.3
How effective is DMF architecture in learning flow map? (Tab. 1, Tab. 2)
How does the representation quality affects the few-step generative modeling? (Tab. Fig.
How can we efficiently train flow map model? (Fig. 4, Tab. 2)
Decoder depth ablation. We analyze the effectiveness of DMF when fine-tuning from flow models. We first train SiT-L/2 model for 400K iterations. then convert into DMF model and fine-tune for 100K iterations. We compare DMF models with McanFlow(MFFGengg follow their setup including model guidance scale. In Tab. 1, we report FID, IS, and FD of fine-tuned MF-L/2 and DMF-L/2 models with different depth. We observe that DMF-L/2 achieves lower FID and FDDINOV2, and higher compared to MF-L/2 when depth is properly chosen. Notably, found depth=18 (i.e., 6 blocks for decoder) performs the best, and depth=16 and depth=20 comparable, which aligns with Fig. 3. When fine-tuned with MG, DMF-L/2 significantly improves 1-step and 2-step performance, and sigmificantly outperforms MF-L/2.
al. 2025b), where strictly
Effect of encoder representation. Furthermore, investigate the effect of representation quality in learning flow map. To this end, we train SiT-L/2+REPA for 400K iterations following (Yu et al., 2025) and fine-tune MF-L/2 and DMF-L/2 model with it. Note that we do use REPA during fine-tuning as it shows diminishing gain. As shown in Tab. 1, both MF-L/2 and DMF-L/2 achieves better performance when initialized with S7T-L/2+REPA, while DMF-L/2 outperforms MF-L/2. The results are consistent when applied with MG. The results show that the encoder representation helps flow map modeling, where DMF architecture achieves higher gain due its design.
Training efficiency. Next, we examine the efficiency of flow-matching warmup. To this end, we compare DMF-L/2 trained from scratch, and DMF-L/2 initialized from SiT-L/2 trained for 400K and 800K iterations. We use same MG config for each training. In Fig. 4, we plot the 1-step FID (NFE= = 1) and training FLOPS for each approach. We observe that the flow models quickly adapts to flow maps, and starting from S/T-L/2 800K model achieves the best performance when using same training compute. We hypothesize that longer flow model training leads to better representation, which helps learning flow map. As of practical consideration, results show that allocating training budget more on flow model training is more efficient, as adapting to flow map is casier yet expensive.
4.2 COMPARISON
Comparison with MeanFlow. Given the observations from Sec. 4.1, we conduct system-level comparison between DMF and MF models of various sizes (B/2, L/2, and XL/2) with same guidance configuration. For DMF models, we train with flow matching loss for 160 epochs, and continue train with DMF loss for 40 and 80 epochs. Tab. 2 compares FID-50K of MF and DMF models. We observe
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Table 2: Comparison with MeanFlow on Ima- geNet x 256. We compare FID of DMF and
Table 3: ImageNet 256x256 benchmark. 2x
denotes usage of CFG and f denotes usage of guid- ance interval (Kynkäänniemi et al., 2024).
MeanFlow (MF; Geng et al. 2025a) models of various size. For each, we apply same guidance as of MF models. FID results of MF models are excerpted from their paper. DMF models do flow matching warm-up for 160 epochs, and fine-tuned for 40 and 80 epochs, i.e., 200 and 240 epochs total, respectively. Note that DMF models require fewer training FLOPs than MF.
Method
NFF
Params
FID
GANs/ / Normalizing Flows / Autoregressive models
StyleGAN-XL (Saner et al., 2022)
166M
VAR-330 (Tian et.l, 2024)
2x10
2B
1.92
MAR-H/2 ot 2024)
2x256
943M
1.55
STARFlow (Gu al., 2025)
1.4B
2.40
Diffusion Flow models
ADM (Dhariwal & Nichol, 2021)
2x250
55-M
10.94
Model
Epochs
NFE
#Params
FID 4
RIN (Jabri ot al., 2023)
LDM (Rombuch et al., 2022)
2x250
1000
410M
400M
3.60
3.42
MF-B/2
240
130M
6.17
SimDiff (Hoogeboon et 2025)
2x512
2.77
U-VIT-H/2 (Ran et all, 2023)
2x50
501M
2.29
DMF-R/2
200
130M
6.08
DiIITT (llatamizadeh al., 2024)
2x250
561M
240
130M
5.63
DIT-XLZZ (Peebles & Xic, 2023)
2x250
675M
2.27
SiT-XL/2 (Ma al., 2024)
2xx200
675M
2.06
MF-L/2
240
459M
3.84
SIT-XL/2+REPA" (Yu al. 2025)
434
675M
1.37
DMF-L/2
200
459M
3.45
Few-step diffusson Bow models
240
459M
3.24
XL/2 (Fruns 2025)
676M
10.60
676M
7.80
MF-XL/2
240
676M
3,43
IMM-XL/2 (Zhou 2025)
2x1
676M
7.77
2x2
676M
3.99
DMF-X1./2
200
675M
3.02
2x4
676M
240
675M
2.83
MF- /2+ (Geng et al., 20256)
2
676M
2.20
MF-XL/2
240
2
676M
2.93
DMF XL/2+ (ours)
675M
2
675M
1.64
DMF-X1/2
240
2
675M
2.56
675M
Table ImageNet 512 benchmark. 2x denotes usage of CFG. denotes usage of guidance
interval (Kynkäänniemi et al., 2024), and denotes usage of AutoGuidance (Karras et al., 2024a).
Method
NFE
PParams
FID
Method
NFE
#Params
FID 1
GANs/ Normalizing Flows / Autoregressive models
Few-step Diffusion / Flow models
StyleGAN-XI (Saner et al., 2022)
1
168M
2.41
STARFlow (Gu et al, 2025)
3B
3,00
sCD-L (Lu & Song, 2025)
778M
2.55
VAR-136 (Tian al., 2024)
2.63
778M
2.04
MAR-I.(1 (1a al,, 2104)
2x64
1.73
SCD-XL (Lu & Song, 2025)
1.1B
2.40
Diffiiion/ / Flow models
L.IB
1.93
SCD-XXL (Lu & Song, 2025)
1.5B
2.28
ADM (Dhariwal Nichol, 2021)
559M
3,85
1.5B
DiaTT (Haataiizaeh
SimDiff (Hougeboom ct al, 2023)
2024)
2x513
1x250
28
561M
2.67
3.02
AYF-S" (Sabour al., 2025)
280M
3.32
DiT-XL/2
Xic, 2023)
280M
1.87
S/T-XL/2 (Ma et 2024)
2x250
675M
2.62
280M
1.70
SYT-XI /EREP/
2025)
460
675M
1.37
DMF-XL/2+ (ours)
675M
2.12
EDME-XXL (Karms et all, 2024bb
2x63
1.58
1.81
675M
1.75
EDME-XXLL (Kynkäšnnicmiic al., 2024)
1.5B
1.40
EDM2-XXL" (Karra et 202
2x63
1.58
675M
1.68
that DMF models trained for 200 epochs achieves lower FID scores than MF models trained for 240 epochs, demonstrating its efficiency in training. Furthermore, DMF models trained for 240 epochs sigmificantly outperforms MF models. In particular, DMF-XL/2 achieves 1-step FID=3.10, achieving state-of-the-ee result on 1-step diffusion / flow models. We also remark that the training FLOPs of each DMF is smaller than MF counterpart, as flow matching is much cheaper than flow map training.
ImageNet benchmark. Following our observation in Tab. 1, we initialize DMF model from longer trained RE/-RPA to explore the limit of DMF model, and conduct fine-tuning with model guidance applied. Then we compare our final model, DMF-XL/B
with other few-step models (Frans et al., 2025; Zhou et al., 2025; Geng et al., 2025b; Lu & Song, 2025; Sabour et al., 2025), diffusion / flow models (Dhariwal & Nichol, 2021; 1; Rombach al., 2022; Jabri et al., 2023; Bao al., 2023; Hatamizadeh et al., 2024: Peebles & Xie, 2023; Ma et al., 2024; Yu et al., 2025; Karras et al., 2024b), and various generative models such as GANs (Sauer al., 2022), Normalizing Flows (Gu al., 2025), and autoregressive models (Tian et al., 2024; Li et al., 2024).
ImageNet 256 666x255 256 comparison. In Tab. 3. we notice that DMF-XL/2 achieves I-NFE FID=2,16 16, significantly outperforms 1-step diffusion / flow baselines, and strong 1-NFE baselines StyleGAN-XL (FID=2.30) and STARFlow (FID=2.40). Furthermore, XL/2+ achieves 4-NFE FID of 1.51, matching performance of
(FID=1.37), while using x 100 less computation.
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2.6
DMF-XL/- (Euler)
Frichet Distance DINOv?
120
DMF-XL 22+ (Ressart
340
210
SREA
Inception Score
FID-50k
320
100
800
2230
1.6
88
144
280
Number steps (NFE)
Number steps (NFE)
Number steps (NFE)
Figure 5: Fuler vs. Restart samplers. We compare Fuler and Restart samplers with DMF-XL//+
trained ImageNet 256x256. FID-50K, Inception score (IS), and Fréchet distance DINOv2 (FDDINOw2) are reported. We plot results for SiT-XL/2+REPA with CFG.
ImageNet 512x512 comparison. We further experiment DMF on ImageNet 512 resolution. Similarly, we train SiT-XL/2+REPA for 400 epochs, and conduct DMF fine-tuning for 140 epochs. Note that we observe training instability during DMF fine-tuning on higher resolution. Thus, we add QK normalization (Dehghani et al., 2023) with RMSNNrm (Zhang & Sennrich, 2019) enhance training stability and image generation fidelity. We refer to Appendix for details. As shown in Tab. 4, DMF-XL/2+ achieves 1-NFE FID=2. 1..2 and 2-NFE FID==1775, outperforming the prior art SCD-XXL (Lu & Song, 2025). Furthermore, X achieves 4-NFE FID==1688 outperforming AYF-S, which uses AutoGuidance (Karras al., 2024a) during distillation to enhance generation quality. The qualitative samples are in Fig. 2 and Appendix H.
Choice of sampler. Lastly, we compare the Fuler and restart samplers on various metrics (FID, IS, and FDDINOv2). For reference, we report SiT-XL/2+REPA results using Heun's method with 128 steps, and guidance interval applied (see Appendix E). In Fig. 5, we plot the results. We observe that DMF-XL/2+ with Euler sampler achieves lower FDDINOv2 than SiT-XL/2+REPA when using NFE larger than 3, while showing slightly higher FID. Furthermore, when with restart sampler, DMF-XL/2+ achieves higher IS and lower FDDINOV2- As noticed in quantitative metrics, find that restart solver generates more diverse samples due to the stochasticity throughout sampling, which qualitatively visualize in Appendix H. We notice that model capable of applying diverse samplers, where there is a trade-off in terms of different metrics, e.g., Euler sampler shows better FID, while restart sampler better scales in terms of IS and FDDINOV2.
5 RELATED WORK
1-step diffusion and flow models. Research on accelerating diffusion models has advanced from both practical and theoretical perspectives. To mitigate the high sampling cost of pretrained diffusion models, distillation-bast
methods have shown strong promise (Salimans & Ho, 2022; Meng et al., 2023; Yin al., 2024b;a; Heek al., 2024). Beyond distillation, consistency models (Song et al.. 2023; Song & Dhariwal, 2024; Lu & Song, 2025; Geng et al., 2025b; Zhou al., 2025) introduced principled approach to learn a single-step denoiser by enforcing consistency constraints across adjacent timesteps. More recently, several works have proposed learning flow maps (Kim et al., 2024; Boffi et al., 2024; 2025; Geng et al., 2025a; Sabour et al., 2025), which generalize consistency models by modeling the transition between arbitrary pairs of timesteps. While prior efforts primarily focus on designing objectives for learning flow maps, our work instead investigates architectural design, drawing the structural similarities between flow models and flow maps.
Decoupled architectures for generative modeling, Another line of work explores decoupled architectures, typically separating encoder and decoder roles, to improve visual generative modeling. Several studies (Yu et al., 2025; Wang & He, 2025; Wang et al., 2025) demonstrate that strengthening the representational capacity the encoder in diffusion transformers (Peebles & Xie, 2023) enhances both scalability and performance of diffusion and flow models. Alternatively, MAR (Li et al., 2024) employs an decoder design for masked autoregressive generation, inspired by the success of MAE (He et al., 2022) in representation learning. Our work shares this emphasis the role of representation, but extends the perspective toward flow map learning, enabling few-step generation while maintaining alignment with underlying flow models.
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6 CONCLUSION
This paper introduces Decoupled MeanFlow (DMF), an efficient and effective method to learn flow maps for fast generative modeling. Specifically, we show that DMF can seamlessly convert flow models into flow maps, and fine-tuning DMF models with flow map training loss achieves high-quality 1-step generative models. We hope our work promotes future research about efficient inference-time scaling, as well as post-training algorithms that can enhance the generation quality and controllability. We discuss limitations and future directions in Appendix G.
ETHICS STATEMENT
Our work advances visual generative AL, which carries potential risks of misuse such disinformation, deepfakes, or biased outputs. We emphasize that our methods are intended for responsible applications, and encourage safeguards like watermarking, dataset auditing, and alignment techniques to ensure safe and ethical deployment.
ACKNOWLEDGEMENT
This work partly supported by Institute of Information & Communications Technology Planning Evaluation (IIT)) grant funded by the Korea government (MSIT) (No. RS-2019-11190075, Artificial Intelligence Graduate School Program (KAIST); No. DS-2004-00509927, Global AI Frontier Lab). We thank Kihyuk Sohn for valuable discussions and insightful feedback throughout the project.
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Biao Zhang and Rico Sennrich. Root square layer normalization. In Advances in Neural Information Processing Systems, 2019. 9, 19
Lingi Zhou, Stefano Ermon, and Jiaming Song. Inductive moment matching, In International Conference on Machine Learning, 2025. 3, 4, 9,
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Published as a conference paper at ICLR 2026
A TRAINING ALGORITHM
We provide a detailed algorithm to train Decoupled MeanFlow model in Algorithm
Algorithm 1 Training Algorithm for Decoupled MeanFlow
Require: Dataset D, flow map uø, weighting function o, learning rate 7) O, constant 0,
time proposal for FM loss (HFM, EFM). time proposal for MF loss (HME PMB+ 2 >: model
(2) y-(1).
guidance scale >> 0, class dropout probability q > 0, guidance interval [loo Ihigh
1: while not converged do
2: Sample (x, y) ~ and drop y with probability
3: Sample 7FM (NFM: ΣTM), /FM < (1 e TIM - 11 and noise 6FM (0,
4: Diffuse Xlpx f- Ko + Oes EPM. and Vieu + 4 Xo + Jeen FFM
5: VFM < Vin (wssu(Xnn fFM. fFM.y) uo(Xen, fPM. fFM) if frmm E Nlow Thigh else Vim
tet
6: Detach gradient VFM f- sg((vrm)
igt
7:
(0) +- log (e-((cas, || (xtexe LFM, (FM)
VFMl + +0) + 6((FM, (FM)
x(1)) 8: Sample N (MMMT MFF 722 N (2) x112
(MMF: 2MF . (1+ (1+ 11-
9:
Let MMF TMF max te), min(miinnne t2), noise EMF ~N(.I) Diffuse XImI t- Ottsa + own CMF, and Viaw + o Xo + d'sne CMF
10:
Jel VMF < VIME + wwuus( (Xtygs , IMF, IMF, y) ux( /MF, (MF) if (MF E [yoo Prigh else Visa tet
11:
12:
Set target S8 VMF (rMF (MF) due and detach gradient UMF de
sg sg(uMP)
(M) log (e (e- ((turr)m))) [ LMP, (MF) uMLll +c) + @((MF, TMF) Compute total loss [(0) t- (0) + (M) Update f + V VoL((), Φ + (
14:
15:
16:
end while
A.1 TRAINING LOSS
The loss weighting is shown be important when training diffusion and flow models. As such, Karras et al. (2020) proposed to adaptively learn the weighting function by casting as multi-task learning problem. In particular, let denote L, be the flow matching loss for timestep Following Kendall et al. (2018), they consider each loss L; as Gaussian distribution modeled standard deviation o where the maximum likelihood estimation of overall loss results in
L.
C C=
C. + log o =
E,
+
(8)
e
where = log of is log-variance. At a high-level, if the model is uncertain about the task at time f, ie., if u, is high, then the contribution of L, is decreased. In practice, they use an MLP layer with Fourier time encoding to model = ((t).
Similarly, we consider the loss for flow map training as L,,,. However, as the flow map loss Li.- is intrinsically of high-variance and prone to the outliers, modeling with Gaussian distribution may be suboptimal. To this end, we consider Cauchy distribution, has heavier tails than Gaussian. Note that the probability density function of Cauchy distribution given
p Do. 7)
where 2a is a location and 7 is scale parameter. Then we model each loss output with additional parameter "tr,, and the maximum likelihood estimation of the overall loss is given by
Ler L Egr log (1 Ler +1)
1
2 log Yt. E,,
log
Ler ettrr
+1)
Mer
(9)
Vt.r
where ur = log y2 and we omit terms for π as it does not affect training. For implementation, we concatenate the positional embeddings of t and r and use an MLP layer to train u,, = o(t, r), which gives us Eq. (6).
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Published as a conference paper at ICLR 2026
A.2
TIMESTEP PROPOSAL
MANIA Asl Ao
A
2.0
1.5
2.0
Denaky
Denaly
1.0
33
66
Time
Time
Thme
(a) (1A, = (-0.4,-0.4) (b) (01, (0.4,-0.4) (c) (fr, (22) (0.4,-0.8) (d) (11, 2 (0.4,-1 111
Figure 6: Time proposal. The probability density distribution of max X1, X2) and min(X1,, X2).
where X1 ~ Loggitoormal 1. 0), and X2 LogiiNorrml 1.0). The red line depicts distribu- tion of TMF and blue line depicts distribution of (MP- We use (d) as our default choice.
As we mentioned in Sec. 3, we sample t and r from the maximum and minimum of two logit- normml distributions. To characterize the distribution, note that for any two independent continuous random variables X, Y with densities fx. fr, and CDFs Fx, Fy. the order statistics give us following:
F max (z) Pr[max( X, Y) < =| (x),
d
Smax(2 = (3)= (x())))))
dz
Foin (2)
5 Pr|X> x 2|= -
Fx(x))( Fy())).
c
Smin (=)
fr(+)]] fr(|)
where fmax: fmin are densities and Fmax: min are CDFs of max(X, and min (X, Y), respectively. We consider logit-normal distribution with location of and scale of 1, i.e., LN(u, 1). Then for two independent logit-normal distributions X, and X2 with scale parameters f4 and μ22 the densities of max(X,, X2) and min(X1, is given follows:
Smax (z) ((logit(2) M11 (logitt) 2) 12) + (logit((2) (2)g(i)) - n2)
z(1 2)
fmin(=) ((logit(=) - 14) 1all--Dloogtt (logit(>> [22 + ((logit(=) - 12) (logit(2) 111)
2(1 2)
where logit(z) = log - (02) 2mm
--= 2/2 (22) = - Φ(u)du. By using the above formula, plot the distribution of max(X1; X2) and min( X1, X2) in Fig. 6 by varying μ4 and μ22 Note that as we increase the gap between 141 and /2, the min(X,, X2) is sampled close to zero.
We hypothesize that choosing close to zero im- proves the 1-step generative modeling. To validate ablation study with identical setup as in Tab. 1, by varying [l1 and 142 Note that (p1, (22 (-0.4,-0.4) the original setup used in MeanFlow (Geng et al., 2025b). As shown in Tab. 5, choosing r closer to zero leads better 1-step performance. By choosing (μ1, (0.44,
Table 5: 1-step results by varying (H1,P2).
this, we conduct
(H1,
FID
FDDINOv2
(-0.4, -0.4)
20.3
78.1
$71.4
(0.4, -0.4)
19.7
78.8
548.2
(0.4, -0.8)
19.6
78.1
540.3
(0.4, -122)
19.3
79.0
531.6
1.2), we achieve the best results, which we use as our default configuration.
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B IMPLEMENTATION
Table 6: Configurations for ImageNet experiments.
DMF-B/2
DMF-1/2
DMF-XL/2
DMF-XI/2+
DMF-XL/2+
Model
Resolution
256x 255
256x
256x256
256x256
512x512
Params (M)
130
458
675
675
675
FLOPS (G)
23.1
80.7
118.6
118.6
524.6
Hidden dim.
1024
1152
1152
1152
Heads
12
16
16
16
16
Patch size
2x2
2x2
2x2
2x2
2x2
Sequence length
256
256
256
256
1024
Layers
12
24
28
28
28
DMF depth
18
20
20
Optimization
Optimizer
AdamW (Kingma & Ba, 2014; Loshchilov & Hutter, 2017)
Batch size
256
.carning rate
lc-4
Adam (31, (82)
(0.9, 0.95)
Adam
1c-8
Adam weight decay
0.0
EMA decay rate
0.9999
Flow model training
Training iteration
800K
800K
800K
4M
2M
Epochs
160
160
160
800
400
Class dropout probability
0.1
0.1
0.1
0.1
0.1
Time proposal μFM
0.0
0.0
0.0
0.0
REPA alignment depth
8
8
REPA vision ecoder
DINOv2-B/14
DINOv2-B/14
QK norm
X
X
DMF flow map training
Training iteration
400K
400K
400K
400K
700K
Epochs
80
80
80
80
140
Class dropout probability
0.1
Time proposal JFM
0.0
Time proposal (FMP PMF)
(0.4.-1.2)
Model guidance scale w
0.5 [0.0, 1.0]
0.6
0.6
0.6
0.6 [0.0, 0.8)
Guidance interval
[0.0, 0.71
[0.0, 0.71
[0.0, 0.71
QK norm
X
X
X
The detailed configurations in Tab. 6. We latent Diffusion Transformer (DiT; Peebles & Xie 2023) as our backbone. We use pretrained Stable Diffusion VAE (Rombach et al., 2022) to compress image with downsampling ratio of 8 and channel dimension is compressed into latent with size 4x32x33 When training flow models with REPA (Yu et al., 2025), the loss function is given by LrM + ACREPA where CREPA is cosine-similarity loss between embeddings of intermediate output of transformer layer and vision encoder outputs. We use 0.5 with 3-layers MLP with SiLU activation (Elfwing al., 2018) for alignment loss following the original implementation. The evaluation of flow models are in Tab. 7.
e.g., 256x256 image
To expedite training, we use Flash-Attention v2 (Dao, 2024) or Flash-Attention v3 (Shah al., 2024). As Flash-Attention kernel do not support IVP computation in pytorch, we follow the approach introduced Lu Song (2025). Specifically, we use the same kernels for forward and backward computation of Flash-Attention, but for JVP computation, we compute the function output and JVP output simultaneously at the forward pass. To this end, we implement the kernel using Triton (Tillet et al., 2019), and merged through t torch. aut ograd. function When compared to non-optimized kernel, e.g., using pytorch's 's native matrix multiplication to compute JVP, we achieve x4 GPU memory savings for ImageNet 512x512 model where the sequence length is 1024.
JVP
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We automatic mixed- precision with brain floating point 16 (BF16) throughout experiments. We find that using floating point 16 (FP16) often incurs instability, especially when training with model guidance. Furthermore, when training ImageNet 512, norm during training, which leads to inferior results. To this end, we apply QK normalization (De- hghani et al., 2023) with RMSNorm (Zhang & Sennrich, 2019) during DMF training, which enhances the training stability as well as generation quality.
observed large variance of gradient
When training with model guidance (MG), note that the guidance scale related to the CFG scale. Specifically, note that for FM loss, we enforce the conditional velocity to achieve
v(x,,t, = V, + w(v(x, y) v(x;, ()) + v(x,,
(v: wv(x,, t)),
(10)
which becomes equivalent to interpolation of v, and unconditional velocity v(x,, f) with guidance scale 1-w" -_- For instance, when using 0.5, this becomes guidance scale of 2.0. While original MeanFlow paper uses complicated choice by introducing additional hyperparameter between V. and CFG velocity, we find applying only MG suffices to achieve good performance. We also tried using distillation (Song & Dhariwal, 2024; Lu & Song, 2025), i.e., using Vig by using the CFG velocity from pretrained flow models, but we did not find performance gain. Alternatively, apply Auto-guidance (Karras al., 2024a), which uses small and under-fitted model for guidance, during flow map distillation as shown in AYF (Sabour et al., 2025), which we leave as future direction. Lastly, we note that applying guidance is crucial in achieving high-quality 1-step generator; for DMF-XL/2+ model trained without MG, it achieves 1-step FID (NFE = 1) of 8.89 and 4-step FID (NFE of 7.87. we apply CFG during inference, 4-step FID (NFE 8) achieves 2.15, which still lags behind the DMF-XL/2+ with MG (FID=1.51 with NFE 4).
interpolate
B.1 ARCHITECTURE
Velocity
Average Velocity
Average Velocity
Final Layer
Final Layer
Final
DiT Block (L D)
DIT Block
DIT x
DIT Block
emb
Patchify
temb
Patchify
temb
Patchify
temb
remb
Nolsed Latent
y eemb
Nolsed
y emb
Nolsed
y emb
(c) Decoupled MeanFlow Transformer Figure 7: Comparison of Diffusion Transformer (DeblPeebles & Xie 2023), MeanFlow DiT
(a) Diffusion Transformer
(b) MeanFlow Transformer
(MFT;Geng et al. 2025a), and Decoupled MeanFlow DiT (DMFT; ours).
Fig. depicts the transformer architectures we used. The Diffusion Transformer computes the condition embedding by sum of class embedding (y embed) and timestep embedding (t embed). For MeanFlow Transformer (Geng et al., 2025a; Zhou et al., 2025), an additional timestep embedding layer is used, and the condition embedding is computed by the sum of y embed, t embed, and embed, where r is the next timestep. Then the condition embedding is fed to all DiT blocks and final layers, e.g. for modulation of outputs from attention layer and feedforward layer with AdaLN (Peebles & Xie, 2023). On the other hand, Decoupled MeanFlow Transformer use same timestep embedding for and computes condition embedding for encoders by sum of embed and y embed, and sum of embed and y embed for decoders. Note that for MeanFlow Transformer, we feed f r as input to the embedding layer, following their observation.
C SAMPLING
We provide details the sampling algorithms for flow models and flow map models. Sampling
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Published as a conference paper at ICLR 2026
with flow models. Given the trained velocity prediction model vo. solving the probability flow ODE (Song et al,, 2021) with Euler's ' method given by
レ + (r - t),,
(11)
where is current timestep and is next timestep. To reduce the discretization error and improve the precision, one can use high-order method (Karras et al., 2022; Lu et al., 2022; 2025). For instance, Heun's 's method is two-stage algorithm that updates the latents as follows:
& X₁ + (r (x),)
X r- t (vo(xe, t) + ve(&r.7))
Alternatively, one can solve the stochastic differential equation (SDE) with Euler-Maruyama method (Ma et al., 2024). Note that the the SDE is given by
dx: vor=vo(xt... () w. Xx, t)dt + Wu dW
va(x,,
(12)
where W, is a reverse-time Wiener process, and wy 0 is arbitrary time-dependent diffusion coefficient, and 8o is an approximation of score function s(x, 1) = v [ogg(((), Note that one can compute the score function using the velocity prediction model for & using following formula:
(xV, d/x,
Sp (Xe, or(a/0 - o,oo))
where 0ge oy are coefficients.
Sampling with flow maps. Given the flow maps ug the Euler sampler updates the samples through solving the ODE, i.e.
x, = X4 + (r - (x,, t,
(13)
and the restart sampler updates the sample through iteratively denoising to the original sample, i.e.,
R x, (,,, t,
(1 r) + re,
where (0, is random Gaussian noise. To facilitate the best of both Euler sampler and restart sampler, one can use the stochastic sampler proposed in CTM (Kim et al., 2024). At high-level, CTM sampler denoises the intermediate timestep E r). then shift the input through forward processes. Formally, this can be written as
g(r,7) x, + Xx + (s t))ul(xitts))
ar x, + or
ar
x,
as
ag
where g [0, x R [0, is a time shifting function that shifts intermediate timestep with stochasticity 7, and ~ (O, I) is random Gaussian. Note that if 8 = 0, it becomes restart sampler, and if becomes Euler sampler. Following CTM (Kim al., 2024), we consider the function s that satisfies
1 = (1 (1-7)
8
(1 (1-7)-1
1 1- 7-
where y [0, is stochasticity hyperparameter. Then have a. 1-7.r and o, a,-o0 0. az r. One can that if 7 1, have (restart sampler), and if y 0, have (Euler sampler). We find that varying improves FDDINOv2 and IS, while increasing FID.
or
Time-distribution shift. Note that for denoising with higher resolution, has been shown that shifting the timestep distribution during sampling enhances the fidelity (Esser et al., 2024). Specifically, let be shifting factor, then the shifted time is given by
tahil st.
(14)
1)t"
for O. In practice, we use uniform time discretization as default and use shift s = 1.0 (i.e., no shift) for ImageNet 256x256 models, and shift 1.5 for ImageNet 512x512.
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Published as a conference paper at ICLR 2026
D EVALUATION
We follow the setup in EDM2 (Karras et al., 2024b) for evaluation. For evaluation, we use NVIDIA H200 GPUs generate 50,000 samples compute FID, Inception score, and FDDINOV2 Note that we use FP32 precision for generation, while using BFI6 shows negligible differences. Here, we briefly overview each metric we used for the evaluation:
FID (Heusel et al., 2017) evaluates the fidelity of generated samples through comparing the feature distances using the Inception-v3 (Szegedy et al., 2016) model. Specifically, we first gather the embeddings of 1.3M training images well generated images. Then we compute the feature distance by fitting into the multivariate Gaussian distribution.
Inception Score (IS) (Salimans et al., 2016) measure the image quality and diversity using the Inception-v3 classifier. Specifically, we compute the cross-entropy between the ground-truth label and the logit output of classifier to compute IS.
Fréchet Distance with DINOv2 (FDDINov2) (Stein al., 2023) also measures the fidelity of generated images, but using DINOv2 (Oquab et al., 2023) as feature encoder. FDDINOv2 is shown be more aligned with human perception. Note that the computation sames FID, but differs by changing Inception-v3 to DINOv2-L/14.
E DETAILED QUANTITATIVE RESULTS
We provide additional evaluation results for flow models (SIT-XL/2+REPA) and flow maps (DMF- XL/2+). First, we show the reproduced results for flow models, and show additional ablation studies on the DMF decoder depth, MG scale, time proposal distribution, and effect of QK normalization for DMF-X1//++ modeels.
Evaluation of flow models. We show the evaluation results of the flow models (ST-XLL/+REPA) For 256 x56 resolution, we re-use the pretrained model from their official repository'? 2 and for 512x512 resolution, trained the model for 400 epochs (see Tab. 6). In Tab. 7, report the FID and FDDINO<2 of each 256x 256 and 512 x512 resolution model by varying the choice of samplers (SDE and ODE), CFG scale, and number of denoising steps (as well total NFE). Note that REPA used Euler-Maruyama SDE sampler with 250 steps, CFG scale 1.8 and guidance interval (Kynkäänniemi al., 2024) on min max] = [0.0, 0.7] as default, which achieves FID=1.422 On the other hand, our reproduction achieves FID=1.41 when using CFG scale of 2.0, and achieves better FID of 1.37 when using ODE sampler (Heun's 's method) with 128 steps (total NFE=434).
Similarly, for ImageNet 512x512, the original paper reported FID=2.08 when trained for 200 epochs by using CFG=1.3 135, SDE sampler with 250 steps. our reproduction, we achieve FID=1.85 when using same configurations, while achieves better FID=1.37 by using Heun's method with CFG=2.0, and guidance interval technique.
Table 7: FID and FDDINOv2 results of SiT-XL/2-REPA models on ImageNet 256x256 and 512x512. The gray colored rows are excerpted from original REPA paper.
Epochs
Resolution
Sampler
CFG
[Imin Amax]
Steps
NFE
FID,
FDpiooa
800
256x256
SDE
1.8
[0.0, 0.71
250
425
1.42
800
256x256
SDE
[0.0, 0.7]
250
425
1.53
71.6
800
256
SDE
[0.0, 0.7]
250
425
62.4
800
256x256
ODE
2.0
[0.0, 0.7]
128
434
1.37
62.6
200
512x512
SDE
1.35
[0.0, 1.0]
250
500
2.08
400
512x512
SDE
1.35
[0.0, 1.0]
250
500
1.85
41.5
400
512x512
SDE
1.8
[0.0, 0.8]
250
449
1.45
36.6
400
512x512
ODE
2.0
[0.0, 0.81
128
460
1.37
32.0
hhttps:// thub. com hyun- yu/ REPA
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Published as a conference paper at ICLR 2026
Evaluation of DMF models. Next, provide additional ablation the effect of depth, MG scale, time proposal distribution, and effect of QK-normalization for DMF-XL/2+ models. Tab. shows the results. First, observe that using MG scale of 0.6 generally shows better performance than MG scale of 0.5. Note that the flow models achieve the best performance when CFG scale of 2.0, which corresponds MG scale of 0.5. On the other hand, DMF model favors slightly higher guidance scale, which we suspect that the few-step models require higher guidance scale to generate high-fidelity sample within few-steps. Furthermore, the base flow models converted to DMF model without fine-tuning achieved the best performance when using depth of 22. However, we observe that using more layers for decoder generally improves the performance. Lastly, we observe that using more aggressive time proposal distribution improves 1-step performance, which consistent with our observation Sec. A.2.
observe that using depth of 20 better than 22. Note that
For ImageNet 512x512 model, we observe that QK normalization significantly helps stabilizing the training, and improves the overall performance. Note that did not find any gain when applying QK normalization to 256 resolution models. Furthermore, we find that it suffices to train for 400K iterations for DMF-XL/2+ 256 resolution model (no performance gain for longer training), while 512 resolution model keep improves its performance for longer training iterations. We find that 700K training iterations show good convergence.
Table 8: FID and FDDINOs2 evaluation of DMF-XL/2+ models on ImageNet 256 256. We vary dmf depth d, MG scale w, and time proposal (uMP (1) (2)) We report 1, 2. and 4-step (NFE=112,4) FID
and FDDINov2 for each training run.
ststep (NFE =
2-step (NFE 2)
4-step (NFE 4)
Iter.
(MME ME
QK-norm
FID
FDDINO12
FID
FDDINOM2
FID
FDDINOK2
DMFFXXL2+ 256x256
200K
22
0.5
(-0.4,-04 -0.4)
2.91
162.9
1.82
92.8
1.70
78.0
200K
22
0.55
(-0.4, -0.4)
2.74
154.3
1.74
83.1
200K
22
0.6
(0044-0.4)
X
2.60
143.9
1.73
73.0
1.54
60.1
200K
20
0.55
(-0.4, -0.4)
2.54
145.8
1.67
82.5
1.50
69.9
200K
20
0.6
(-0.4,
X
2.46
133.0
1.71
71.5
1.50
60.2
200K
20
0.55
(0.4,-1.2)
2.50
140.4
1.68
85.7
1.60
72.6
200K
20
0.6
(0.4,-13 -1.2)
X
2.25
128.2
1.69
74.6
1.53
63.7
400K
20
0.6
(0.4,-1.2)
2.16
122.3
1.64
69.8
1.51
59.9
-M/-X1/2+
512x512
200K
20
0.6
(0.4.-1.2)
2.97
93.5
2.01
54.8
1.87
43.2
400K
20
0.6
(0.4.-1.2)
X
2.71
86.9
1.95
52.3
1.80
41.6
200K
20
0.6
(0.4,-1.2)
V
2.50
84.2
1.94
53.3
1.84
44.2
400K
20
0.6
-1.4.-1.2)
2.28
77.7
1.87
50.9
1.79
42.1
700K
20
0.6
(0.4.-1.2)
2.12
72.3
1.75
43.9
1.68
39.5
CTM-y sampler. We provide additional evalua- tion of DMF-XL/2+ model when using stochastic CTM sampler. We follow the setup illustrated in Appendix C. As shown Tab. 9, we observe that Euler sampler (i..,, 7=0) achieves the lowest FID, while adding stochasticity improves FDDINO>2 and IS, e.g. 7=0.96 achieves lowest FDpiNov==4..9, and 7=0.98 achieves highest 0S.0...0.. Thus. adding stochasticity through CTM sampler helps generating diverse samples, and improves semantic fidelity, while deterministic Fuler sampler achieves the best FID, which is consistent to Fig.
Table 9: NFE-4 CTM sampler with various 7.
7
FID,
FDDINO
ISt
0.00
1.51
60.0
280.1
0.01
1.75
55.8
283.2
0.02
2.12
53.8
283.1
0.04
3.12
55.7
274.0
0.10
7.79
93.8
219.3
0.50
31.7
335.5
83.3
0.90
5.55
61.6
291.6
0.96
3.03
326.8
0.98
2.39
50.0
328,0
0.99
2.17
52.8
326.6
1.00
1.99
56.8
322.7
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Published as a conference paper at ICLR 2026
F ADDITIONAL OBSERVATION
(wol ST-U2 (400K)
DWF
ST-- (BO0K)
SIT-L/--RPP REU-RREPAAAA (400K)
28
25
FID 50K
24
FID 500
26
23
20
23
12
18 20
12
165
20
12
16
20
Depth
Depth
Depth
Figure 8: Strong flow models are better flow map. We compare the gap between flow model and DMF converted flow map by varying the flow model. We show results for SiT-L/2 trained for 400K and 800K iterations, and SiT-L/2+REPA trained for 400K iterations. FID-50K is reported by sampling with 16-step Euler sampler without using CFG.
As shown in Fig. 3, the DMF model converted from pretrained flow model often outperforms flow model without fine-tuning. We further analyze this phenomenon in details. To study, we exploit SiT-L/2 models trained for 400K and 800K iterations, and SrT-L/2+REPA model trained for 400K iterations. We vary the depth of DMF model by 12, 16, 18, and 20, similar to the setup in Tab. 1.
As shown Fig. 8, we find that the DMF models from SiT-L/2 400K model do not show gain in compared to their base model. However, training proceeds, the DMF model from S/T-L/2 800K starts to outperform its base model by setting appropriate depth. Furthermore, we notice that DMF model significantly outperforms when initialized from SiT-L/2+REPA 400K model, even trained for only 400K iterations. We hypothesize that this is due to the representational capacity of base flow model in turning to flow map. As training proceeds, it is well-known that the model forms representational knowledge, thus SiT-L//2 800K model tends to be better flow map than SiT-L/2 400K model. On the other hand, if we explicitly align the model with self-superviser representation, the model quickly forms the representation, which helps to form better flow map.
G DISCUSSION
Limitations. Although our method demonstrates substantial improvements in FID, IS, and FDDINOK2, we frequently observe visual artifacts in generated samples, particularly under the 1- step setting. We attribute this issue partly to the constraints of our current experimental setup, which relies on the VAE latent space and the ImageNet dataset, both of which contain inherent quality limitations. As next step, it would be valuable to validate the effectiveness of DMF on large-scale text-to-image (Esser al., 2021) and text-to-video (Wan et al., 2025) models.
Future directions. We believe approach opens promising line of research toward efficient training and inference of diffusion and flow models. For example, reducing inference cost may enable re-examination of scaling laws for diffusion models (Esser et al., 2024; Blattmann et al., 2023; Yin et al., 2025), allowing more compute to be allocated per denoising step. Another promising direction inference-time scaling (Ma et al.. 2025), such as searching over initial or intermediate noise states using Restart solvers. Finally, extending post-training algorithms, which have so far been mainly studied for diffusion and flow models (Wallace et al., 2024: Lee et al., 2025; Liu et al., 2025; Xue et al., 2025), to flow maps remains an open challenge.
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H QUALITATIVE EXAMPLES
(a) 1-step
(b) 2-step Euler sampler
(c) 2-step Restart generation
(d) 4-step Euler generation
(c) 4-step Restart generation
Figure 9: Generation with with class id 33: loggerhead turtle
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(a) 1-step
(b) 2-step Euler sampler
(c) 2-step Restart generation
(d) 4-step Euler generation
(c) 4-step Restart generation
Figure 10: Generation with DMF-XL/2+-512 with class id 291: 1ion
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Published as a conference paper at ICLR 2026
(a) 1-step
(b) 2-step Euler sampler
(c) 2-step Restart generation
(d) 4-step Euler generation
(c) 4-step Restart generation
Figure 11: Generation with MMF-XL/2+-512 with class id 388: panda
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Published as a conference paper at ICLR 2026
(a) 1-step
(b) 2-step Euler sampler
(c) 2-step Restart generation
(d) 4-step Euler generation
(c) 4-step Restart generation
Figure 12: Generation with DMF-XL/2+-256 with class id 89: sulphur-crested cockatoo
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Published as a conference paper at ICLR 2026
(a) stspp
(b) 2-step Euler sampler
(c) 2-step Restart generation
(d) 4-step Euler generation
(c) 4-step Restart generation
Figure 13: Generation with -M2-X2 with class id 360: otter
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Published as a conference paper at ICLR 2026
(a) 1-step
(b) 2-step Euler sampler
(c) 2-step Restart generation
(d) 4-step Euler generation
(c) 4-step Restart generation
Figure 14: Generation with XMF-XL/2+255 with class id 933: cheeseburger
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Reviews:
[{"review_id": "XU0NkBRl65", "reviewer": "Reviewer_Rqpx", "summary": "This paper mainly proposes an alternative time-conditioning design for MeanFlow models, named decoupled MeanFlow (DMF). Instead of modifying the architecture of a flow model to accommodate two timesteps,  DMF treats the DiT as an encoder-decoder architecture, and feed $t$ to the encoder and $r$ to the decoder, which leads to notable gains in generation quality. Combining this design with other technics such as flow matching warm-up, adaptive weighted Cauchy loss, and representation alignment, DMF achieves the state-of-the-art 1-step FID of 2.16 on ImageNet 256x256.", "questions": "In L208, it is stated that feeding the next timestep to both the encoder and decoder is redundant, which motivates DMF. Why would redundancy cause issues for the model? Neural networks are generally redundant by design, so I do not really understand the intuition of why feeding the timestep to selective blocks would be better than feeding it to all the blocks, apart from the concerns of architecture modifications.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The central contribution of this work is the simple time conditioning modification. This leads to notable performance gains as shown in the ablation studies in Table 1 and 2, validating the effectiveness of the decoupled design.\n- Overall, a 1-step FID of 2.16 on ImageNet 256x256 is an impressive state-of-the-art result.", "weaknesses": "- This work is motivated by the encoder-decoder design. Yet the experiments does not provide direct evidence to prove that encoder-decoder is the key to high quality. For example, there are many other ways to condition the network without modifying its architecture, like interleaving $t$ and $r$ for the DiT blocks. Discussing alternative design choices in the ablation could strengthen the argument.\n- The authors claim that an existing SiT can be converted into a flow map without finetuning, yet the results in Fig. 3 only show a very minor gap between DMF and SiT. Sometimes it's even worse than the baseline (Fig. 8 left). The slight improvement in general is unsurprising since the flow map tends to be closer to the average of start- and end-point velocity, thus it's reasonable that mixing start and end time in the model should be better than the plain SiT baseline.\n- FM training with REPA is not really something new. It's not surprising that initializing from REPA models generally improves MF and DMF, which is not unique to DMF. Thus its relevance to the main contribution is weak.\n- Writing issues: \n  - Flow models trained on random noise-data pairs predicts the expectation of $\\alpha_t^\\prime x_0 + \\sigma_t^\\prime \\epsilon$, i.e., $v(x, t) = \\mathbb{E}[\\alpha_t^\\prime x_0 + \\sigma_t^\\prime \\epsilon]$. The definition of $v(x, t)$ in L146 is not accurate.\n  - Metric consistency: L422 says \"DMF-XL/2 achieves 1-step FID=3.10\", yet table 2 shows FID=2.83.", "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": "8TZoQCkVpj", "reviewer": "Reviewer_9NpD", "summary": "The paper proposes Decoupled MeanFlow (DFM), a method to accelerate diffusion or flow models by converting them into flow maps which can do large denoising jumps. DMF decouples the model's architecture into an encoder and a decoder, where only the encoder receives information about the start of the jump and only the decoder receives information about the end of the jump. DMF achieves the state-of-the-art performance on ImageNet, outperforming shortcut models, MeanFlow models and GANs.", "questions": "See weaknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The proposed DMF model consistently outperforms the MeanFlow baseline across all evaluated datasets and variants. Notably, it achieves high-quality 1-step ImageNet generation which highlights its efficiency and strong generative capacity.\n- The model can be trained from scratch, yet it also seamlessly integrates with existing pretrained models without requiring any architectural modifications while yielding improved results. \n- The analysis of the encoder–decoder decomposition is interesting. It is particularly noteworthy that a pretrained model, when utilized under the proposed scheme and without any training, can outperform the original model in few-step generation regimes.", "weaknesses": "- While the separation of encoder and decoder components is appealing, it also seems natural to consider joint conditioning mechanisms that integrate information from both the current and target timesteps in some blocks, potentially via lightweight modifications such as joint AdaLN conditioning or LoRA adapters. Have the authors explored such hybrid alternatives?\n- Given that MeanFlow already incorporates both timestep conditionings, one might expect the model to implicitly learn to attenuate or emphasize the relevant conditioning at different stages (e.g., down-weighting target timestep signals early and source signals later). Why does the explicit disentanglement in DMF lead to consistently better results? A more detailed discussion or theoretical analysis on this would strengthen the conceptual clarity of the 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": "4P99qxCMpu", "reviewer": "Reviewer_1Fiu", "summary": "The authors explore architectural improvements for training flow map models and propose a series of techniques to enhance the performance of MeanFlow under comparable compute budgets. The resulting Decoupled MeanFlow (DMF) framework introduces a decoupled encoder–decoder design that enables pretrained flow matching models to be seamlessly converted into flow map models without architectural modification. By conditioning the decoder on the next timestep while keeping the encoder focused on the current one, DMF improves both efficiency and transferability of pretrained representations. This approach, combined with flow-matching warm-up, adaptive Cauchy loss, and tailored timestep sampling, achieves state-of-the-art few-step generative performance on ImageNet 256×256, reaching a 1-step FID of 2.16 and matching standard flow model performance at 4 steps.", "questions": "1. **Representation quality**\n\nDoes the proposed decoupled architecture improve the representation quality of the transformer encoder itself compared to vanilla MeanFlow (e.g., linear probing accuracy) under similar training budget?\n\n2. **Diminishing gains with REPA**\n\nThe paper notes that REPA fine-tuning yields diminishing returns (Tab. 1). Could the authors provide quantitative comparisons (apply REPA only for MF fine-tuning or apply REPA at both stages) or intuition on why representation alignment offers less benefit under the DMF design or consistency training in general?\n\n3. **Loss formulation**\n\nWhen doing MF fine-tuning, the authors use sum of MF & FM losses instead of batch splitting proposed in MeanFlow. However, the adaptive weighting function itself breaks the \"correctness\" of the FM objective (e.g., the optimal solution is no longer $\\mathbb{E}[v | x_t = x]$). Have the authors evaluated DMF performance with the vanilla flow-matching loss without such weighting for ablation, and how does it compare in stability and convergence?\n\n4. **Timestep sampling**\n\nHave the authors experimented with alternative timestep proposal paradigms (e.g., $p(t, r) = p(t)p(r | t)$)?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. **Training-free flow map transformation**\n\nThe proposed decoupled architecture allows pretrained flow models to be directly repurposed as flow maps without additional fine-tuning, which is both conceptually elegant and practically impactful. This demonstrates a viable paradigm for transformer-based flow map models that leverages existing large-scale flow model checkpoints, reducing training cost and broadening applicability.\n\n2. **Broader applicability of the fine-tuning paradigm**\n\nThe proposed fine-tuning strategy has strong practical implications. Because DMF can be directly initialized from large-scale pretrained flow checkpoints (e.g., FLUX-dev, SD3, etc.), it enables transforming existing models into few-step generators with a modest additional compute budget. This makes the method immediately applicable in real-world or large-foundation-model scenarios where retraining from scratch is infeasible.\n\n3. **Comprehensive empirical validation**\n\nThe paper includes detailed ablations, consistently validating the design claims, particularly the benefit of decoupling timestep conditioning and the effectiveness of flow-matching warm-up for stability and efficiency.", "weaknesses": "1. **Stability of the JVP term**\n\nThe proposed method does not directly address the well-known stability issue of the JVP term. This instability has been repeatedly identified as the primary bottleneck in scaling consistency-based methods to large-scale applications such as text-to-image or text-to-video generation (Lu & Song, 2024; Chen et al., 2025; Zheng et al., 2025). Therefore, while the techniques presented in the paper for improving MeanFlow training remain valuable, the overall scope of the paper remains somewhat limited. It would nonetheless strengthen the paper to include an empirical comparison of training stability between DMF and vanilla MeanFlow (e.g., visualizations of training losses, gradient norms, or JVP magnitudes).\n\n2. **Insufficient ablations**\n\nThe use of the adaptive weighted Cauchy loss (Eq. 6) for MeanFlow optimization is intriguing but under-justified. The paper should better explain why this choice improves robustness beyond prior alternatives (e.g., the adaptive normalization proposed in Geng et al., 2024 and the tangent normalization proposed in Lu & Song, 2024) with supporting evidence. Also, the paper should cite Dao et al., 2025, as they also proposed applying a near identical Cauchy loss to consistency training.\n\n3. **Limited architectural exploration**\n\nWhile the encoder-decoder design for training-free flow map transformation is intriguing, the current experiments primarily rely on the vanilla DiT. It remains unclear whether the encoder–decoder decoupling generalizes to other variants of DiT (i.e. LightningDiT (Yao et al., 2025) or DDT (Wang et al., 2025)), and the paper would be greatly strengthened from some discussions of this.\n\nLu, Cheng, and Yang Song. \"Simplifying, stabilizing and scaling continuous-time consistency models.\" arXiv preprint arXiv:2410.11081 (2024).\n\nChen, Junsong, Shuchen Xue, Yuyang Zhao, Jincheng Yu, Sayak Paul, Junyu Chen, Han Cai, Song Han, and Enze Xie. \"Sana-sprint: One-step diffusion with continuous-time consistency distillation.\" arXiv preprint arXiv:2503.09641 (2025).\n\nZheng, Kaiwen, Yuji Wang, Qianli Ma, Huayu Chen, Jintao Zhang, Yogesh Balaji, Jianfei Chen, Ming-Yu Liu, Jun Zhu, and Qinsheng Zhang. \"Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency.\" arXiv preprint arXiv:2510.08431 (2025).\n\nGeng, Zhengyang, Ashwini Pokle, William Luo, Justin Lin, and J. Zico Kolter. \"Consistency models made easy.\" arXiv preprint arXiv:2406.14548 (2024).\n\nWang, Shuai, Zhi Tian, Weilin Huang, and Limin Wang. \"Ddt: Decoupled diffusion transformer.\" arXiv preprint arXiv:2504.05741 (2025).\n\nYao, Jingfeng, Bin Yang, and Xinggang Wang. \"Reconstruction vs. generation: Taming optimization dilemma in latent diffusion models.\" In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 15703-15712. 2025.\n\nDao, Quan, Khanh Doan, Di Liu, Trung Le, and Dimitris Metaxas. \"Improved training technique for latent consistency models.\" arXiv preprint arXiv:2502.01441 (2025).", "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": "LsPvKtren2", "reviewer": "Reviewer_9VuX", "summary": "The paper proposes Decoupled MeanFlow (DMF), a way to convert a pretrained flow (or diffusion-as-flow) model into a flow-map model without changing the backbone: treat the early blocks as an encoder conditioned on the current time $t$ and the late blocks as a decoder conditioned on the next time $r$. This decoupling lets the model learn the average velocity between $(t,r)$ while reusing the original timestep embedding and velocity head. With a flow-matching warm-up then flow-map fine-tuning (plus model-guidance and a robust Cauchy loss), DMF targets ultra-few-step sampling (1–4 steps).", "questions": "1. Table 1 suggests both model guidance (MG) and REPA are crucial for DMF’s final performance. DMF typically splits at later layers (e.g., layer 18), whereas REPA often targets earlier layers (e.g., layer 8 in SiT-L/2). Is there a principled relationship between the REPA alignment layer and the DMF encoder–decoder split?\n2. The paper mentions visual artifacts in generated outputs in limitations. Could you include representative ‘bad-case’ examples to illustrate these failures?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. This paper proposes simple, compatible architecture. The key idea—drop $r$ from the encoder and $t$ from the decoder, i.e., $u_\\theta(x_t,t,r)=g_\\theta(f_\\theta(x_t,t),r)$—is elegant and backbone-agnostic, enabling plug-and-play conversion of existing flow models.\n\n\n2. Strong empirical case that “your flow model is secretly a flow map.” Without any finetuning, the converted model can already outperform the base SiT in FID at equal step counts; with decoder-only finetuning it gets further gains. The depth ablation is informative.\n\n\n3. State-of-the-art 1–4 step results under fair comparisons. Tables show consistent wins over MeanFlow baselines at comparable training budgets, and competitive/best few-step FIDs on ImageNet 256/512.", "weaknesses": "See Questions", "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)