Blockwise Flow Matching: Improving Flow Matching Models For Efficient High-Quality Generation
Authors: Dogyun Park
Taehoon Lee
Minseok Joo
Hyunwoo J. Kim
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion; Flow matching; efficient generation
Primary area: deep_learning
TL;DR: We propose blockwise flow modeling framework that aim for optimal Pareto-frontier between generation performance (FID) and inference complexity (FLOPs).

Abstract: Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations.
Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost.
Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance.

Blockwise Flow Matching: Improving Flow Matching Models For Efficient High-Quality Generation
Dogyun Park Korea University gg9330korea ac.
Taehoon Lee
KAIST (1xogus1830kaist.ac.k
Minseok Joo Korea University #lgkcjf87@kkore.. ac kr
Hyunwoo J. Kim KAIST
byunxoojkimskaist... ac kr
Abstract
Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across wide range of domains. It typically employs single large network to learn the entire generative trajectory from noise to data. Despite their effectiivnness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256 x 256 demonstrate that BFM establishes substantially improved Pareto frontier over existing Flow Matching methods, achieving 2. 2.1x x to 4.9x accelerations inference complexity at comparable generation performance. Code is available at https://gihab..co//illlbbb//
Introduction
Recent advances in generative modeling have been driven by the success of diffusion and flow- matching frameworks [1-4], which learn to transform noise into high-quality data through sequence of denoising steps. Powered by advanced transformer architectures [5, 6]. these approaches have expanded the frontiers of high-fidelity data generation across many fields, including images [7-10], 3D data [11-14] and videos [15-19]. In particular, the Flow Matching (FM) framework [3, 20-22] has emerged as a simple effective training paradigm, adopted by several models [23, 24].
generative
common design choice in FM models is to use a single large neural network to learn the entire velocity field, from noise data. While parameter-efficientt, this monolithic design faces key limitations. First, the generative trajectory from noise to data inherently involves distinct signal characteristics across time [4]: frequency-domain analysis (Figure shows that early timesteps
"Corresoondngg author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Siugk Velecky Medel
MDTV2-XL
SITXL
FID (lower is better)
REPN-XL
12
XLa (Ours)
X0
A1
c W
BF 3FM-XLLr-44 (Qurs)
Vanilla Matching
Vilecto Blakk
Valedio Block
Black
Bllck
4.5x mort officiont
2.1 more efficent
2500
5000
7500
10000 12500 15000 17500 20000
Matching (Ours)
FLOPs (G) (lower better)
Figure I: Blockwise Flow Matching (BFM) achieves more favorable Pareto-frontier between generation performance (FID) and inference complexity (GFLOPs) on ImageNet 256 x 256. While standard Flow Matching models train a single model, our BFM partitions the flow trajectory into distinct temporal segments, each handled by smaller but specialized velocity block, improving generation quality and efficiency.
are dominated by irregular, low-frequency patterns, while later timesteps require modeling refined, high-frequency details. This temporal heterogeneity imposes conflicting demands on single shared model, limiting its ability to effectively capture both coarse global structure and subtle local variations simultancously. Second, using model must be evaluated at every solver step, resulting in a total computational complexity of ((SK), where S' is the number of steps and K is the model's 'ss size in FLOPs. Together, these limitations make challenging to balance the trade-off between sample quality and inference efficiency.
large model across timesteps incurs high inference costs, the full
To address these challenges, we propose Blockwise Flow Matching (BFM), novel framework that rethinks the monolithic architecture of standard FM. Instead training a large, shared model, BFM partitions the flow trajectory into distinct temporal segments, each handled by smaller, specialized velocity block (Figure 1). This segmentation strategy allows each block to focus on a narrower temporal window and better adapt to the specific signal characteristics, supported by our spectral power analysis (Figure 6). As a result, BFM not only improves generation quality but also reduces inference cost by activating only subset of the model each timestep.
However, temporal segmentation limits each block's 's exposure clean signals, potentially restrict- ing their capacity to learn high-level semantic features. To mitigate this, we propose Semantic Feature Guidance (SemFeat), module that explicitly conditions each velocity block on semantic features aligned with powerful pretrained encoders, such as DINOv2 [25] (Figure 2a). SemFeat significantly enhances the generation fidelity, a cost of increased computation. reduce this, we propose additional lightweight module, Feature Residual Approximation, which efficiently approx- imates semantic features during inference, preserving sample quality while significantly reducing computational cost (Figure 2b and 2c).
Through extensive experiments on ImageNet at 256 x 256 resolution, we demonstrate that BFM establishes a more favorable Pareto frontier, achieving substantial improvements in both generation quality and inference efficiency over existing ofate-of-the-ar flow matching methods (Figure 1, Table 2). Notably, we achieve comparable or better generation quality with a 2./x to 4.9x reduction in inference complexity compared to current pest-performing models [26], highlighting the effectiveness of our proposed components.
Our main contributions summarized follows:
We propose Blockwise Flow Matching (BFM), novel framework that divides the generative trajectory temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise modeling improves both generation quality and inference efficiency.
We introduce Semantic Feature Guidance and Feature Residual Approximation modules that significantly enhance visual fidelity while preserving efficiency gains enabled by BFM.
Extensive experiments demonstrate that BFM achieves a substantially improved Pareto frontier on ImageNet 256 x 256, yielding 2.1 to 4.9x x faster inference than state-of-the generative models with comparable performance.

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2 Related Work
2.1 Diffusion and Flow Matching models
Diffusion models [1, 2, 15, 27, 28] have emerged as powerful tools for generative modeling, achieving state-of-the-arr performance across diverse domains [4, 13, 15, 29-31J. More recently, Flow Matching (FM) [3, 20, 21, 32] has been proposed as general framework that unifies and extends diffusion- approaches. By directly modeling continuous-time velocity fields between noise and data, FM enables simulation-free training with improved stability and sample quality. Building on this foundation, transformer-based FM architectures like SiT [22] and FiT [6] have achieved strong performance across various generative tasks. However, these models remain computationally expensive at inference time, due to their large model size and the need for repeated evaluations across solver steps. In parallel, there has been growing interest in integrating semantic representation learning into generative models [26, 33, 34J. For instance, RCG [33], REPA [26], and DDT [35] show that semantic features from pretrained visual encoders (e.g., CLIP [36] or DINO [25]) can significantly improve generation fidelity. While these approaches enrich representations, they does not consider distinet characteristics at different diffusion timesteps and are computationally inefficient. In contrast, our method introduces Blockwise Flow Matching with our SemFeea module, enabling efficient and high-quality generation.
2.2 Efficient generation
Recent research has explored various strategies to improve the inference efficiency of diffusion and flow-based generative models. One direction involves distillation-basee methods, such consistency models [37-42], distribution matching distillation [43-46], which aim to reduce the number of solver steps by training a student model imitate the behavior of pretrained teacher. While effective in accelerating generation, these methods require strong teacher models, multi-stage optimization, and in some cases, adversarial training, which can increase both training complexity and instability. Our method is orthogonal to these approaches and could benefit from distillation techniques to further accelerate generation. Another line of work focuses on model-based compression, which reduces per-step computation by streamlining the network architecture. Prior works such as token merging [47], token pruning [48]. and layer pruning [49] propose removing redundant computation during inference. Recently, dynamic inference approaches [50, 51] have introduced input- or timestep- aware mechanisms to adjust the computational graph during generation. However, these methods rely on a single shared model to handle the entire generative trajectory. In contrast, our method partitions the generative trajectory into multiple temporal segments, each modeled by a smaller, specialized velocity block. BFM is complementary to pruning and dynamic routing strategies, which could be applied within individual blocks to further improve efficiency.
3 Preliminary
Diffusion and flow-based models [1-3,20] aim to learn continuous transformation between simple reference distribution To (e-g.. Gaussian noise) and target data distribution TT. Given samples To ~ To and x IT, the transformation is defined over continuous time interval / E [0, 1] by the following ordinary differential equation:
dæ: dt
v(ze, t).
(1)
where 2, denotes time-dependen interpolation between zo and œ1, and v Rd x [0, velocity field defined over the data time joint domain. The interpolation is formulated as:
1] +
Rd is the
2₁ ~ N(a of where an = 01 =0, 0,
a1 = 0 = 1.
(2)
Different choices of interpolation coefficients a and o; yield different instantiations of diffusion or flow models [20, 52]. Following recent practices [22],
adopt a linear interpolation schedule: a, = and o, = - t. To learn the velocity field, a neural network ti is trained to approximate the ground-truth conditional velocity field by minimizing the mean squared error:
min Emg, []]o(z,, t) va(z, =)
This formulation is commonly referred to as the standard flow matching framework for training continuous-tima generative models.
3

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(a) Blockwise Flow Matching with Semantic Feature Guidance Section 4.1 & 4.2)
Pretrained Encoder
X
Alignment Network
hip
Lalign
hip (fr)
Xg
X
Velocity Bluck
(m)
Xg
LBF
(b) Feature Residual Approximation ( Section 4.3)
(c) Inference Section 4.4)
lightweight FRN
lightweight FRN
x
m
Alignment Network
FRN
O-
mm
LFRN
Alignmeni
ft
Network
Figure 2: Overall pipeline of our method. (a) Blockwise Flow Matching partitions the flow trajectory
into M segments, each modeled by a specialized velocity block 1n ((())) Semantic Feature Guidance enhances the velocity block by explicitly conditioning features fe from the feature alignment network Ja. (b) After training velocity models and Se. we freeze them and train the Feature Residual Network (FRN) to efficiently approximate ft by residual connection. (c) During inference, samples can be efficiently generated by evaluating fo once per segment, reducing inference complexity.
4 Method
4.1 Blockwise Flow Matching (BFM)
Standard Flow Matching (FM) models [3, 20, 22] train a single large neural network model the entire flow trajectory from noise to data. However, this design imposes two key limita- tions. First, it forces network simultaneously handle the distinct spectral characteristics at different timesteps [4, 53]. As illustrated Figure 3, early timesteps are dominated by irregular, low-frequency signals, while later timesteps contain more structured, high-frequency content. This gives conflicting demands a single model, which may struggle to represent them effectively. Second, it results high inference cost, as the full model must be evaluated at every solver step, yielding a total complexity of O(SK), where is the number solver steps and K is the model's size in FLOPs.
0.6
Le
40
High Freqeency Rantio
Spectral Entropy
50
Hig feeuuro
0.0
0.0
02
0.4
0.5
0.5
1.0
Figure 3: Spectral entropy (SE)
and high-frequency ratio across timesteps.
To address these limitations, we propose Blockwise Flow Matching (BFM), which partitions the flow trajectory into sequence of specialized velocity blocks of model size K",
each focusing on distinct temporal segment. By dedicating each block smaller temporal region, these blocks can efficiently capture interval-speciff dynamics, allowing the use of smaller networks with size K' < K. Consequently, each timestep. only the corresponding block is evaluated, reducing the inference complexity. Formally, consider flow trajectories defined from pure noise at timestep & 0 to clean data timestep 1. We divide this interval into M non-overlapping
segments defined by intervals {[tm-1, bm 1 where to < f ... < Lt = and each
segment is modeled by its velocity block (m) To train the m-th block segment [tm- fm),

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Table I: Component analysis: progressively adding components our BFM-S backbone. All models are trained for 100K iterations and evaluated using the 250 ODE Euler solver without classifier-free guidance. FLOPs are averaged across solver steps and number of samples. indicates that lower values are better. Values in parentheses denote relative performance compared to the vanilla FM model (SiT-S). Implementation details are the supplementary material.
Solver steps
Avg. Params/step
Total
Method
GFLOPs 4
FID 4
Params
Vanilla Flow Matching (SiT-S (22])
5.45 (x1)
82.6
246
33M
33M
Vanilla BFM-S (M = 6)
3.64 (x 1,50)
81.5 (-1.1)
246
18M
99M
SemFeat (BFM-Ssp)
5.01 (x1.09)
66.9 (-15.7)
246
23M
70M
+Residual approx. (BFM-SSFRA)
2.96 (x1.84)
68.3 (-14.3)
246
16M
75M
define the corresponding start and end points of the segment by interpolating between a clean data sample and Gaussian noise sample:
Start: Tim-1 (1m 1 (1 12)
(4)
End: Tt... ~ - (4mm1, , (1 lm 21)
(5)
We sample noise for Equation (4) and (5) to enhance the straightness of the flow trajectory across segments. For a randomly sampled t E m1 tm). we sample intermediate data 2, as:
(1 - a. (tm((t)))z (t)) + am (f)
where am (1) (t- 1m-1mm///// ()m the m-th segment is given by:
mm). Then, the ground-truth conditional velocity at time t within
(m) dæ.
Ft.. 2tm
dt
I.
1m-1
We train each block og (m) to predict the target velocity using the blockwise flow- fow-matching loss:
(or = Eza.zi.t [116) (mm) (sx, (xe, (v (/ 1
8
where denotes optional conditioning information, e.g., class labels. We omit for notation simplicity. During inference, given current state 2, and timestep t, evaluate only the corresponding velocity block (("") As empirically demonstrated in Table 1, our proposed BFM-S with six segments (second row) reduces overall inference complexity (FLOPs) while improving generation quality (FID) compared to the standard FM baseline (SiT-S [22]) using the identical transformer blocks.
4.2 Semantic Feature Guidance
While our blockwise modeling enables efficient inference and segment-wisg specialization, the temporal scope of each velocity block restricts its exposure the clean data distribution. In particular, blocks operating in early timesteps primarily observe noisy samples, making it challenging to capture high-level semantic features. Motivated by recent studies [26, 33, 34] demonstrating the effectiveness of semantic representations in generative performance, we propose semantic conditioning technique, called Semantic Feature Guidance (SemFeat), which enhances each velocity block by conditioning rich semantic context fo. (Figure 2a).
Specifically, introduce shared feature alignment network fa which aims extract robust semantic features from noisy intermediate states v,, To ensure these extracted features carry strong global semantic information, we train this alignment network by aligning its output features with embeddings from pretrained visual encoder ε, such as DINOv2 [25]. Given an intermediate noisy input x, timestep I, the alignment network produces semantic feature: fi fa c), where fg : Rd= (0, 1) x Rd: Rd= and dR denotes conditioning information. This feature is trained to match the pretrained embedding h = E(x1) by minimizing the following feature alignment loss:
Calign(d, v) = Er.. a [d (fo(fflxzr c)), h")],
(9)
where hy is the learnable projection MLP layer to match the dimensionalities, and d(-,-) distance metric such cosine similarity. Then, the velocity block 1g
(m) takes the current state
5

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Figure 4: Samples from BFM-XL SF ImageNet 256 with classifier-free guidance (w 4.0).
Tr. timestep t, condiction c, and semantic feature f. as inputs to estimate the conditional velocity (oz, C, ft). The blockwise flow matching loss with the semantic feature guidance
field: a!()) un (mm)
becomes:
[|o(m)) - m/(m))1)
LBrM (6, Φ) Erg.
(10)
Finally, the overall training objective weighted sum of the blockwise flow matching and feature alignment losses:
C LAFM Aaaiign
(11)
where Ả controls the contribution of the feature alignment objective. Refer to Algorithm for training pseudo code. This conditioning strategy allows each block to access semantically rich guidance, significantly improving generation quality. As demonstrated in Table 1, integrating SemFeet into
BFM (third row in Table I) achieves substantial FID gains compared to the vanilla BFM.
Comparision with REPA [26]. Our SemFeat is inspired by recent works in representation -aiggned diffusion, particularly REPA. However, there is key difference in design: REPA aligns the internal hidden states of the velocity model directly with semantic features. In contrast, SemFeat introduces a dedicated alignment network fg whose output explicitly conditioned on the velocity blocks, thereby separating feature alignment from velocity prediction. We observe that this modular design leads to more coherent and rich representation (Figure 8) and improved generation quality (Table 6).
4.3 Feature Residual Approximation
The feature alignment network fo significantly improves generation quality by providing rich semantic guidance. However, evaluating the alignment network at every timestep during inference can undermine the efficiency gains by our BFM. To address this, we propose training a lightweight network that enables efficient approximation of semantic features during inference (Figure 2b).
Specifically, after the initial training phase where we jointly optimize the feature alignment network fø and the velocity blocks vo, we freeze the parameters of both sets of networks. Then, in a second training stage, we introduce a smaller network fn, denoted as Feature Residual Network (FRN), to approximate semantic features within the m-th temporal segment [4m= lm). This is motivated by the observation Figure that the discrepancy between start point feature ft... and intermediate feature Se increases as increases within (mm-11 mm).
Given the start point Itm-1 we first compute its corresponding semantic feature using the alignment network: ftm-: = fo c). For the subsequent timestep t where t E [tmm tm), we approxi- mate its feature incrementally via residual connection defined by: = fim-, ; + (t) (x c). f-tm-1 is normalized offset from fm-1- This allows the network f, to seale the where (t) = T-.-t=-
residual contribution based on how far the timestep / is from the segment start point fm FRN fn trained to match the output of the frozen alignment network fo intermediate timestep f, i.e..
ft føl c), using the following feature regression loss:
LFRx(T) = E [ 12
(12)

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Table 2: System-level comparison on ImageNet 256 x 256 caass-oondiiooee generation with classifier-free guidance [28, 58]. FLOPs are averaged across the solver steps and number of samples. 4 and f indicate whether lower higher values are better, respectively. use of guidance scheduling.
Method
Epochs
# #Params.
Step
GFLOPs
FID
IS t
Pre.
Rec. 1
ADM [59]
400
554M
250
1120
3.94
186.7
0.82
0.52
CDM [27]
2160
4.88
158.7
LDM-4 [4]
200
400M
250
104
3.60
247.7
0.87
0.48
VDM++ [60]
560
2.40
225.3
[61
240
501M
113
2.29
263.9
0.82
0.57
MDTv2-XL. [62]
1080
675M
129.6
1.58
314.7
0.79
0.65
MaskDiT [63]
1600
675M
2.28
276.6
0.80
FlowDCN [64]
400
618M
2.00
263.1
0.82
0.58
SimpleDiffusion [65]
800
2B
2,44
256.3
SD-DIT [34]
480
3.23
FiTv2-3B [6]
400
3B
250
653
2.15
276.3
0.82
0.59
FiTv2-XI. [6]
400
671M
250
147
2.26
260.9
0.81
0.59
DiT-XL |5]
1400
675M
250
114.5
2.27
278.2
0.83
0.57
SiT-XL [22]
1400
675M
250
114.5
2.06
270.3
0,59
REPA-XI. [26]
800
675M
250
114.5
1,80
284.0
DiffMoF-I. [51]
600
458M
250
2.13
274.3
0.81
0.60
DyDiT-XLA=0.7 [50]
678M
250
84.3
2.12
284.3
0.81
0.60
DyDiT-XIxx005 [50]
678M
250
57.9
2.07
248.0
0.80
0.61
BFM-XLsv (Ours)
400
942M
246
107.8
1.75
289.4
0.82
0.61
BFM-XLSF-RAA (Ours)
600
1038M
246
37.8
2.03
278.1
0.80
0.62
By leveraging this lightweight residual approximation, we drastically reduce inference cost, since the feature alignment network fo is only computed once per segment, and subsequent semantic features within each segment are computed efficiently by the FRN (see Figure 2c). Empirically, our analysis demonstrates that this residual approximation (third row in Table 1) retains over 98% of the BFM-Sst fidelity while reducing inference complexity by 41% % (5.01 to 2.96). Refer to Algorithm 2 for pseudo code.
4.4 Inference
At the beginning of the m-th segment, we compute the semantic feature fim-1 using the feature alignment network fa. For subsequent timesteps E [4m-1, (m)) ). approximate the semantic feature either using FRN fn or the full alignment network /o. depending on the desired trade-off between speed and fidelity. Then, the velocity block v/ intermediate state is updated iteratively via a numerical solver using the predicted velocity. This process repeats until reaching implementation of the inference process is provided in the Appendix (Algorithm 3 and 4).
(m)) predicts the velocity: o!!m) eg (m) (æx, c. ft). The
yielding the final sample 21 Piat- A full pseudocode
Experiment
We primarily compare our method with recent flow matching models built on diffusion transformer architectures [S, 6, 22, 26), demonstrating stateoofthhe-a performance in generative tasks. We follow the experimental setup established by SiT [22] and REPA [26]. Most of the experiments are conducted the ImageNet dataset at resolution of 256 256, unless stated otherwise. We utilize an off-the-sher pretrained VAE from Stable Diffusion [4], which applies an 8x downsampling factor. We evaluate generation quality using several established metries, including FID [54], sFID [55], Inception Score (IS) [56], Precision, and Recall [57]. Following recent architectural best practices [5, 6, 22], we adopt a DiT-style transformer backbone for both Up. fo. and fT. To integrate conditions to ng, we sum the semantic feature fi with the timestep embeddings element-wise and inject it at the attention layers via
modulation [5]. Our model configurations are based on and -XI. architectures with patch size of 2 and M 6. More implementation details are available in the Appendix A.
7

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5.1 Comparison with state-of-the-arf models
In Table 2, we present a comprehensive comparison of our Blockwise Flow Matching (BFM) framework against recent state-of-the-art generative models. Our BFM with Semantic Feature Guidance (BFM-XI-gt sp) achieves an FID score of 1.75, surpassing closely related diffusion transformer models such as F [6]. DIT [5], SiT [22], and REPA [26]. Notably, compared to the previous best-performing model, REPA, our model demonstrates consistent improvements across FID and IS with notable improvement of IS by 5.4 points, while also reducing inference complexity in terms of FLOPs by approximately 5% (from 114.5 to 107.8). Furthermore, by incorporating our efficient Feature Residual Approximation module BBFM-XLSFRRA we achieve inference efficiency gain, a 67% reduction in FLOPs over REPA, corresponding to roughly a 3 speed-up. When benchmarked against the recent crccueecy-oousee model, DyDiT-XLA [10], our BFM-XL not only reduces inference complexity from 57.9 to 37.8 GFLOPs but also significantly improves generation quality, reflected by 30.1 points increase in IS. These results highlight our model's ss superior capability in balancing both generation performance and inference efficiency compared current state-of-the-an approaches.
more substantial
Few-step sampling. We further evaluate model's performance under a small number of solver steps in Table 3, essential setting for achieving ef- ficient and practical image generation. In real-world scenarios, reducing the number of function evalua- tions (NFEs) directly translates to faster sampling and lower inference cost, often the expense of gen- eration quality. Remarkably, BFM-XLsF achieves an Inception Score of 248.2 and FID of 8.01 using only six solver steps, demonstrating strong robust- ness with minimal degradation as the number of steps decreases. In contrast, SiT-XL and REPA-X -XL exhibit substantial performance drops of 91.1 and 122.8 in Inception Score, respectively, whereas BFM- XLsr shows much smaller reduction of 62.8. Furthermore, BFM-XL-sF attains an FIDD of 8.01, outperforming SiT-XL, and REPA-XL by large margins of 4.9 and 5.01 FID points, respectively. These results indicate that BFM maintains high-quality generation even under extremely low NFE settings, validating its effectiveness for fast and resource-efffcient inference. We attribute this superior few-step performance to the coherent and semantically rich representations provided by our Semantic Feature Guidance, which stabilize the velocity field and enable more consistent dynamics even at early timesteps, as visualized in Figure 8
Table 3: Generation performance for differ- ent number of solver steps. indicates the absolute degradation in performance.
Method
Step
18
4
FID
A
SIT-XL
250
270.3
2.06
179.2
91.1
12.91
10.85
250
305.7
1.42
REPA-XL
182,9
122.8
13.02
11.6
BFM-XL
246
315.4
1.36
248.2
62.8
8.01
6.65
5.2 Generalization and Scalability
Compatibility to MeanFlow To further demonstrate the effectiveness of our method, we integrate BFM into the recently proposed MeanFlow [66], which enables high-quality generation using only a few solver steps. Specifically, we adapt our approach by constructing four specialized velocity blocks corresponding to the four-step diffusion trajectory in MeanFlow and applying the MeanFlow objective independently to each temporal segment. This design allows each block to learn distinct dynamics across the generative process, enabling efficient sampling with only four function evaluations (one per segment). As summarized in Table 10, our integrated model 4FFMsr+MeanFloww achieves substantially lower FID of 9.7 compared to the Mean baseline of 13.2, despite using the same number of sampling steps. This result highlights the strong compatibility of BFM with existing few-step generative frameworks and demonstrates its effectiveness in improving both efficiency and sample quality with lower inference cost.
Training at higher resolution. To examine the scalability of our approach to higher image resolu- tions, we compare our model against the SiT baseline on ImageNet at 5122 resolution. For this setting, we adopt the S-architecture configuration with patch size of 4. The results, summarized in Table 1 clearly demonstrate that our BFM with Semantic Feature Guidance substantially outperforms the SiT baseline, achieving a remarkable 14.69 improvement in FID. This consistent improvement at a higher resolution highlights the robustness and scalability of our framework in capturing fine-grained visual details and maintaining semantic coherence across larger spatial resolution.
8

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Table 4: Ablation on the number Table 5: Ablation on the number Table 6: Comparison of our pro- of segments with fixed number of segments with fixed total posed SemFeat and REPA [26] on of layers per segment.
network capacity.
FM and BFM framework.
Seg. Lay.
FLOPs (G)
FID
Seg. Lay.
FLOPs (G)
FID
Method
FLOPS
FID
(G)
3.64
85.1
5.46
81.7
3.64
81.5
6
8
3.64
81.5
FM REPA
5.45
72.9
3.64
79.1
8
6
2.72
88.1
FM SemFeat
6.88
68.5
12
3.64
76.7
12
4
1.82
95.2
(c) BPM SemFeet
5.01
Law frequrccy
Frivker detsssnure
Rosikal
MSF
Btck1/ Bonk
Power Spectrum
000
High frequeacy
02
05
10
Kesss
Average MSE
8.54
8.53
Real SIT (laselin))
RPM (Chrs)
1000
Black number
Spatial Frequency
Training steps
Figure 5: Discrepancy between fim-1 and ft within each block averaged over 50 samples.
Figure 6: Fourier power spec- trum of real images, SiT- generated images, and BFM.
Figure 7: Training loss CERN over time with and without fea- ture residual approximation.
5.3 Analysis
To show the efficacy of our components, we conduct comprehensive component-win wise analysis.
Effeet of temporal segments. First, we investigate how varying the number of temporal segments M in BFM influences generation quality and computational efficiency under two complementary settings. This analysis provides insight into how temporal decomposition affects specialization and scalability within the dow-matching framework.
1) Fixed per-segment capacity: In Table 4, we fix the number layers within each segment while varying the total number of segments M, thereby keeping the per-segment capacity constant. We observe that increasing M consistently improves FID scores, suggesting that finer-grained temporal partitioning enables each velocity network to specialize more effectively in modeling localized dynamics along the generative trajectory. Importantly, these improvements come without any increase in inference complexity, highlighting BFM's ability to scale up without added inference cost.
2) Fixed total network capacity: In Table 5, we fix the overall model capacity by increasing the number of segments while proportionally decreasing the number of layers per segment. This setup demonstrates trade-off: while more segments provide greater temporal specialization, shallower blocks may lack sufficient capacity to model complex signals. Empirically, we find that moderate segmentation level (e.g.. g. M 6) achieves the optimal balance, allowing for effective specialization while preserving sufficient expressiveness within each block.
Spectral analysis. To further investigate whether blockwise modeling promotes specialized learning across different stages of the generative trajectory, conduct frequency-domain analysis of generated images. Following the methodology [67], we compute the 2D Fourier power spectrum for both real and generated images and apply azimuthal integration to derive their mean spectral power distributions. This analysis allows us to assess how well each model captures structural details across spatial frequencies, from coarse global layouts to fine- anniinede textures.
As illustrated Figure 6, the Fréchet distance between the spectral distributions of real images and those generated by BFM-XLsF (0.049) is smaller than that of SiT-XL (0.054), indicating that our model more faithfully reproduces the frequency characteristics of natural images across the spectrum. This result supports core design hypothesis: segment-wiss specialization enables different blocks

---

t=0
BFM-XLg
BFM-XL
VER
Figure 8: Semantic features over timesteps. We visualize the PCA of features from BFM and REPA for the source images. Compared to REPA, the semantic features extracted from BFM are more con-
Figure 9: Generated images from BFM without (left) and with (right) Residual Approx- imation.
sistent across timesteps.
to more effectively capture diverse signal characteristics across the diffusion trajectory, leading to improved spectral fidelity.
SemFeat vs. REPA. We analyze the effectiveness of our proposed SemFeat by comparing it against the closely related approach, REPA [26]. As discussed in Section 4.2, SemFeat differs from REPA in a key design: SemFeea leverages an external feature alignment network that explicitly conditions features on the velocity model, whereas REPA aligns semantic features implicitly within the velocity model itself. This modular design separates representation learning from generative modeling, enabling SemFeat learn more coherent and stable semantic representations.
To empirically validate this, we conducted a feature-level analysis by applying Principal Component Analysis (PCA) the semantic features fi extracted from each model. We visualize the top three components in Figure 8: SemFeat exhibits high semantic consistency across varying noise levels, capturing temporally stable and semantically meaningful information. In contrast, REPA generates noticeably noisier and less consistent semantic features, even within the same object region, highlighting the advantage of SemFeet''s modular conditioning. Quantitative comparisons in Table 6 confirm these observations. Starting from standard FM with REPA (a), replacing REPA with SemFeat (b) yields a significant FID improvement of 4.4 points, underscoring the effectiveness of explicit modular conditioning. Moreover, integrating SemFeat within our BFM framework (c) further improves the FID score by an additional 1.6 points, while reducing inference complexity.
Effectiveness of feature residual approximation. To demonstrate the effectiveness of our feature residual approximation approach, we first compare it against direct approximation method that independently predicts semantic features, i.e., f. = fy( c) without residual connections. Figure 7 shows that our residual approximation method converges faster and achieves lower feature approxi- mation loss (CrRn), highlighting the efficacy of modeling semantic features residual increments from the segment's start point. Additionally, as demonstrated in Table and 2, incorporating resid- ual approximation significantly reduces inference complexity: BFM-Sy--R reduces 41% FLOPs compared to BFM-SsF and BFM-XLSI-RA reduces 65% FLOPs compared to -LL- all while preserving generation quality. Qualitative visual comparisons in Figure 9 also demonstrate marginal perceptual differences, validating efficient feature approximation.
6 Conclusion
In this paper, we introduced Blockwise Flow Matching (BFM), novel generative framework that partitions the generative trajectory into distinct temporal segments, each handled by compact and specialized velocity blocks. This design allowed each block effectively capture the unique signal characteristies of its interval, leading to improved generation quality and efficiency. By further incorporating our proposed Semantic Feature Guidance and Feature Residual Approximation modules, we demonstrated that BFM establishes a significantly improved Pareto-frontier between generation performance and inference complexity on ImageNet 256x256: 2.1 and 9x9x acceleration in inference complexity compared to the existing state-of-the-art generative methods.
10

---

Acknowledgement
This work was partly supported by the National Supercomputing Center with supercomputing resources including technical support(SSC-02--CCE-222, 30%). the Korea Research Institute for defense Technology planning and advancement-Grre funded by Defense Acquisition Program Administratioon(DAA., (KRIT-CT-23-021, 30%), the Institute of Information & communications Technology Planning (Valuation(IITP) grant funded by the Korean government 00457882, Research Hub Project, 30%), and (RS NSS-2025-22 2025-25442149 LG Al Star Talent Development Program for Leading Large-scale Generative Al Models in the Physical Al Domain, 10%).
(RS-2024
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A Implementation details
Table 7: Architecture and training configurations of Blockwise Flow Matching
Vanilla BFM-S (Table
BFM-SkF
BFM-SSF-RA (Table 1)
BFM-XL (Table 2.3,5.7-10)
BFM-XI
(Table 1,4.6.7.12)
(Table 2,8,10)
Num. segments M
6
Each Velocity Block ug
Num. layers
Hidden dims
384
384
1152
1152
Num. heads
16
Feature Aligument Network Jo
Num. layers
6
6
20
20
Hidden dims
384
384
1152
1152
Num. heads
6
6
16
16
Feature Residual Network Jn
Num. layers
Hidden dims
384
1152
Num. heads
16
Training Config.
Optimizer
Adam
Adam W le-4
Adam le-4
AdamW le-4
Adam le-4
Learning rate
le-4
Batch size
864
864
864
864 0.5
864
A
0.5
Visual Encoder 8
DINOv2-B cosine sim.
DINOv2-B cosine sim.
DINOv2-B cosine sim.
DINOv2-B cosine sim.
d(---)
We provide the overall hyperparameter setup in Table 7.
Training. We implement our model based the original SiT implementation [22] with recent improvements such as SwiGLU [68] activations, RMS normalization [68]. and Rotary Positional Embeddings (RoPE) [69]. Following FiTv2 [6], we reassign model parameters and adopt AdaLN- LoRA [70] within transformer blocks to mitigate the parameter overhead of AdaLN modules. This adjustment substantially reduces the total parameter count while maintaining comparable perfor- mance.
We pre-computed latent vectors derived from pixels via the Stable Diffusion VAE, without applying data augmentation, following [26]. For feature projection, we employ a three-layer MLP with SiLU activations. We adopt uniform temporal partitioning with L. 22 for simplicity, though preliminary experiments indicate that non-uniform, data-adaptive partitioning could further improve performance. To train multiple velocity networks across temporal segments, one simple approach is to randomly sample a velocity network per iteration: however, this may lead to uneven updates among networks. Instead, we uniformly divide each training batch according to the number of temporal segments and assign corresponding timesteps to each subset. For example, with batch size of 256 and four temporal segments, each segment receives 64 samples. This training strategy ensures balanced updates across all velocity networks and reduces training variance by evenly sampling timesteps across the entire time horizon. All experiments are conducted with global batch size of 864 using eight NVIDIA A100 GPUs. Full training pseudocode is provided in Algorithms and 2.
Training complexity. Our Blockwise Flow Matching (BFM) be viewed form of sparse activation, analogous to a Mixture-of-Experts (MoE) model with a fixed router, where each velocity network serves as an expert. Similar MoEs, BFM increases the total parameter count while maintaining comparable computational cost and latency. We evaluate the training resource usage on ImageNet 256 256 for XL configuration using NVIDIA A100 GPU with batch size of 32. We use deepspeed profiler to measure the FLOPs and results are summarized in Table 8, We use multiply-accmmulate (MACs) represent FLOPs. For both simple and balanced training strategies, BFM achieves per-iteration FLOPs and training throughput comparable to SiT and REPA. Although BFM introduces more parameters, its memory footprint increases only moderately (from 30-31 GB to 47 GB), remaining well within the capacity of modern GPUs. These results demonstrate that BFM both practical and scalable for large-scale training. Furthermore, is possible to train each block parallelly (and separately) across multiple GPUs, which further improve the training scalability.
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Table 8: Training efficiency. Per-iteration com- putational cost, throughput, and memory usage. indicates our balanced training strategy.
Table Inference efficiency. Wall-clock run- time and total FLOPs at 256x256 resolution with 246 NFEs.
Method
TFLOPs Iters
Mem. (GB)
Method
NFE
Runtime
GFLOPs
STT-X/2
7.59
2.54
30
SIT-XL2
246
44,51
114.5
REPA-XL/2
7.72
2.62
REPA-LL XL/2
246
44.51
114.5
BFM-XL/2 (Ours)
7.47
2.78
45
BFM-XI/22r (Ours)
246
40.37
107.8
BFM-XL/2 (Ours)
7.71
2.24
47
BFM-XL/2EER (Ours)
246
19.42
37.8
Table 10:
Compatibility MeanFlow [66]
Table 11: System-level performance comparison on ImageNet 512² resolution for 400K training iterations. Method
framework on ImageNet 256² for 400K train- ing iterations.
Model
NFE
FID 1
FID
NFE J
McanFlow
13.2
SIT-S/4
102.54
246
3PPMs++MeanEin
9.7
BFM-S/4 (Ours)
87.85
246
the Euler solver with the ODE (Tables 1,3,4,5,6 in the main paper) or the Euler-Maruyama solver [22] with the SDE (Table in the main paper). We keep the 246 solver steps (41 solver steps for each segment) except for Table 3 in the main paper.
Inference. For inference,
Specifically, given an initial noise input Ito Zo Pnoise the generation proceeds sequentially through each temporal segment fm)) At the beginning of the m-th segment, we compute the semantic feature fi.-, using the feature alignment network fa- For subsequent timesteps t E (m)) we approximate the semantic feature either using FRN fn or the full alignment network [a. depending on the desired trade-off between speed and fidelity. Then, the velocity block ((m)
0/ predicts the velocity: a!!m) vig (mm) (x1, ft). The intermediate state is updated iteratively via numerical solver using the predicted velocity. This process repeats until reaching t = 1, yielding the final sample I1 Pdata- A full pseudocode implementation of the inference process provided in Algorithm and 4.
Inference complexity. We benchmark the wall-clock inference time of models against baseline methods on single NVIDIA A100 GPU with a batch size of 32. The results are summarized in Table 9. Empirically, our primary model, BFMsF. achieves 9.4% 4 reduction in inference time than the baselines while attaining better FID scores. Furthermore, the most efficient variant, BFM achieves remarkable 63% reduction in runtime while maintaining performance comparable to SiT. These results demonstrate that the reduction in FLOPS achieved by BFM translates directly into real-world speedups, validating its inference efficiency.
Metrics. We evaluate generation performance using standard metrics including FID [54] (Fréchet Inception Distance), IS [56] (Inception Score), and Precision/Recall [57, 71J. Unless otherwise noted, we follow the evaluation protocol of [59] and report results using 50K generated samples.
FID is the most commonly used metric, measuring the feature distance between real and generated image distributions. It is computed using the Inception- V3 network under the assumption that both feature distributions follow multivariate Gaussian statistics.
IS, also based on Inception- V3, evaluates both image quality and diversity by measuring the KL- divergence between the marginal and conditional label distributions derived from the network logits.
Finally, Precision captures the fraction of generated samples that lie close the real data manifold, while Recall measures how well the generated distribution covers real data samples. Together, these complementary metrics provide more holistic assessment of generative performance in terms of both fidelity and diversity.
B Analysis details
Component analysis (Table 1). We provide additional implementation details for the experimental configurations reported in Table of main paper. For the vanilla Flow Matching model, train
17

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Algorithm
Training Blockwise Flow Matching (BFM)
Require:
Feature alignment network Sex velocity network vs, and projection layer hi:
repeat
2: Sample a mini-batch of size B: {(mb) (8)
))
zb. data, 21 noise
3: Initialize losses: LUrM <- 0, Lalign
4: Partition sample indices i uniformly into M disjoint groups: Ii..... IMM
5:
for each segment m ...... M do for each sample index E Im do
6:
> All samples can be computed parallel
7:
Sample g(() ~ m, tm) (i)
8:
+ (1 )0-1) + 11
9:
(1 4m (m0 + 1
(6)
(6)
am (t)(0)
( -mm
24 (1)
(1-mm(tt())z))
am am) ((()) t fo (0)
Im 1m
Semantic featturs: (0(()) t E(x1)),
(
11:
(0)
12:
Segment velocity target: 1/2
(m)
Itm 3tm-1
hm 1m-1
Per-sample losses:
Calign += d ( h²()))
14:
15:
LBFM += || (m)) (8)
c((() 1:
m (m,))) 112
16:
end for end for
17:
Normalize losses: L + (CEEM + X Calign)
18:
19:
Update 0, Φ, u with gradient step on until convergence
20:
Algorithm 2 Training Feature Residual Network (FRN)
1:
Freeze parameters 10, J hy, and introduce FRN parameters f
2:
repeat
3:
Sample
1111.... M]
4:
Sample t ~ 11 (m, tm)
5:
Compute semantic feature segment start: ft,. (are .1 So (xit, c)
6:
Compute semantic target at intermediate step 1: St.
7:
Compute normalized time offset 6m (t) Em 1m- -1
8:
Approximate semantic feature at intermediate step ft fem-1 + b fr(
9:
Compute residual approximation loss CFRN = Ilfi - fell
10:
Update FRN parameters 17 via gradient step on CIRN until convergence
11:
the original SiT-S model (12 transformer blocks) with architectural improvements. For our vanilla BFM-S model (second row of Table 1), we train the same transformer architecture (except that we reassign model parameters with AdaLN-LoRA) with six temporal segments. We assign each velocity block with 8 transformer blocks. When adding a feature alignment network (BFM-Ssr., third row of Table 1), we reduce the number of layers of each velocity block, as shown in Table 7.
Spectral Entropy and High-Frequency Ratio (Figure 3). To analyze the frequency characteristics of generated images across timesteps, we compute two key metries: Spectral Entropy (SE) and the High-Frequency Ratio (HFR). Spectral Entropy quantifies the distributional complexity of a signal in the frequency domain. Specifically, we treat normalized 2D power spectrum of an image as probability distribution and compute its Shannon entropy. A higher SE indicates more uniform, less structured distribution of spectral energy (i.e., more randomness). while a lower SE reflects concentration of energy in fewer frequencies, indicating more structured signals. High-Frequent
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Algorithm 3 Inference
1: Initialize: Σtg = Zn ~ Pnoise
2: for m 2,,,....
...; M do
3: Define K solver steps within segment: 1m-1 = (10) < < ((K) mm
4: for k: 0, 1, ,..,, K 1 do
5:
Compute semantic feature: fa(0 = fo(
Compute velocity: dRc,) up 1/mh (z f((e))
6:
7:
Update state with solver & step size Al:
8:
12(k = (Fr00), ( At)
9:
end for end for
11:
Output final generated sample: 1 Pdata
Algorithm 4 Efficient inference with Feature Residual Network
Initialize: Tta = Tig ~ Proise .... MM do
2: for m = ...,
3: Compute semantic feature once at segment start:
4:
ftm-; = f (x
5: Define K solver steps within segment: 1m-1 (10) ((K) Im
6:
for = 0, 1, K do
Compute normalized time offset bm (1(8)) ((4) (14)-mm-1
7:
im 1mm-
8:
Approximate semantic feature efficiently: fec = fem-i + (m(((()) ff(exas).)
(mm) (I few)
9:
Compute velocity: θςcn) 1/g
10:
Update state with solver d step size At:
11:
Fx((+1) (I,,0, (r00) At)
12:
end for
13:
end for
14:
Output final generated sample: 01 ~ Pdata
Ratio measures the proportion of total spectral energy in the high-frequency range. It captures the relative contribution of one-grained details the image.
To compute both metries, we randomly sample 10,000 real images from the Image set and transform them to noisy versions specific timesteps by interpolation formulation. Each image is converted to the frequency domain via a 2D Fourier Transform. We then calculate the power spectrum and apply azimuthal integration obtain the spectral distribution. SE is computed as the Shannon entropy of the normalized spectrum, while HFR is obtained by summing the energy above predefined frequency threshold (=0.5) and dividing by the total energy.
Fourier power spectrum (Figure 6). We perform frequency-domale analysis evaluate how well the spectral characteristics of generated images match those of real images. This experiment tests whether our blockwise modeling strategy improves spectral fidelity by allowing different blocks to specialize in capturing distinct frequency components along the generative trajectory. Specifically, we randomly sample 100 images from each model (BFM-XL,) and SiT-XL [22]) and 100 real images from ImageNet. We compute the 2D Fourier power spectrum for each image and apply azimuthal integration to obtain ID mean spectral power distribution, following the procedure in [67]. We then calculate the Fréchet Distance [72] between the spectral distributions of generated and real images to quantify their similarity.
Discrepancy between ftm-, and fo (Figure 5). For each segment m, we randomly sample 50 images from the ImageNet dataset and convert them into their corresponding noisy versions Ztm-- and r, at timesteps (m-1 and I. [1m=1, (mm), respectively We then evaluate the temporal consistency of the semantic features extracted by the alignment network by computing the mean squared error (MSE) between ftm.. = [ c) and fe = [a c). lower MSE indicates that the feature alignment network learns temporally stable, time- iime-invariant representations across the segment.
19

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Quantitative comparison between REPA [26] and SemFeat (Table 6). We provide additional implementation details for the experimental configurations reported in Table All models are trained for 100K iterations using DINOv2-B [25] as the target representation, with a loss weight of X = 0.5 and negative cosine similarity as the alignment objective. Feature projection layers are implemented with identical configurations across all methods for a fair comparison. (a): We implement REPA using the SiT-S architecture (12 transformer layers), aligning the hidden representations at the 8th transformer layer to the DINOv2-B targets. (b): We incorporate
proposed SemFeat into the standard FM framework by decomposing the SiT-S model into two modules: feature alignment network composed of 8 transformer layers, and velocity model composed of 4 transformer layers. (c): This setting corresponds to our BFM-Sxp in Table 7.
PCA results (Figure 8, 10) For the PCA analysis, extract semantic features from noisy inputs It using both REPA-XL and BFM-XLsF- In the case of REPA-XL, we use the hidden representations from the 8th transformer layer, this layer is aligned with DINO features during training. For BFM-XLsIE. we directly use the outputs of the feature alignment network, ft = fo (zt, c). We perform Principal Component Analysis across features collected from multiple timesteps dominant variations. The top three principal components are then mapped to the RGB channels for visualization, allowing assess the semantic consistency and structure of features across time.
capture their
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C Additional PCA results
In Figure 10, present additional PCA visualizations of semantic features across varying noise levels. SemFeat consistently produces semantically coherent and temporally stable representations, maintaining structural consistency even under significant noise. In contrast, REPA exhibits greater variability and noise in its feature representations, with noticeable inconsistencies across the same ob- ject regions. These observations further support the effectiveness of SemFeat's modular conditioning in capturing robust and meaningful semantic information throughout the generative trajectory.
icarg
1
RUPA
SOIEDO Itaae
inaaee
source inagee
0-
source icange
SEPA
0
1
REPA
Figure 10: Semantic features timesteps. We visualize the PCA of features from BFM and REPA for the source images. Compared to REPA, the semantic features extracted from BFM are more consistent across timesteps.
21

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D
More qualitative results
Figure 11: Uncurated generation results of BFM-XIsE- We use classifier-free guidance with 4.0. Class label "fox squirre!"
Figure 12: Uncurated generation results of BFM-XL We use classifier-free guidance with w 4.0. Class label "Cacatua ga- lerita" (89).
(335).
Figure 13: Uncurated generation results of BFM-XL We use classifier-fir free guidance with w 4.0. Class label "shield, buckler" (787).
Figure 14: Uncurated generation results of BFM-XLsp. We use classifier free guidance with 4.0. Class label "snow leopard" (289).
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Figure 15: Uncurated generation results of BFM-XLSF. We use classifier-free guidance with 4.0. Class label "American robin"
Figure 16: Uncurated generation results of -FM-XL We use classifier-free guidance with 4.0. Class label "volcano" (980).
(15).
Figure 17: Uncurated generation results of BFM-XI SF. We use classifier-free guidance with w 4.0. Class label "Great Dane
Figure 18: Uncurated generation results of
BFM-XL We classifier-free guidance with w = 4.0. Class label = "green mamba" (64).
(246).
23

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Figure 19: Uncurated generation results of BFs-XL We use classifier-fre free guidance with w = 4.0. Class label = "Cliff" (972).
Figure 20: Uncurated generation results of BFM-XLsr. We use classifier-free guidance with w = 4.0. Class label "Coral Reef" (973).
Figure 21: Uncurated generation results of BFM-XLSE. We use classifier-free guidance with w = 4.0. Class label = "Alp" (970).
Figure 22: Uncurated generation results of BFM-XLsE We use classifier-free guid- ance with w = 4.0. Class label = "Lakeside" (975).
24

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Figure 23: Uncurated generation results of BFs- We use classifier-free guidance
Figure 24: Uncurated generation results of BFM-XLSF. We use classifier-free guidance with w 4.0. Class label "Norwegian elkhound, elkhound" (174).
with 4.0. Class label "bald eagle, American eagle, Haliaeetus leucocephalus" (22).
Figure 25: Uncurated generation results of BFM-XI sr. We use classifier-free guidance with w = 4.0. Class label "hippopotamus, hippo, river horse, Hippopotamus amphibi- ous" (344).
Figure 26: Uncurated generation results of BFM-XL sp- We classifier-free guidance with w 4.0. Class label = "lesser panda, red panda, panda, bear cat, bear, Ailurus fulgens" (387).
25

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Figure 27: Uncurated generation results of BFM-XL We use classifier-free free guidance with w = 4.0. Class label = "altar" (406).
Figure 28: Uncurated generation results of BFM-XLsr. We use classifier-free guidance with w = 4.0. Class label = "castle" (483).
Figure 29: Uncurated generation results of BFM-XI We use classifier-free guidance with 4.0. Class label "coffee mug"
Figure 30: Uncurated generation results of
BFM-XL.F. We use classifier-free guidance with 4.0. Class label "library" (624).
(504).
26

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E Limitations and Future work
Reliance on external features. Our method relies on semantic features extracted from a pretrained visual encoder (e.g., DINOv2) to guide the velocity models through SemFeat. While this enables stronger semantic conditioning and improves generation quality, it introduces an external dependency and limits the model's s generality to domains where such pretrained encoders are available. In future work, we plan to explore self-supervised alternatives that jointly learn semantic representations during training, potentially eliminating the need for external networks.
Multi-modal large-scale datasets. Our current evaluation focuses single-modality image gen- eration using ImageNet. While BFM scales well in this setting, applying the same framework to multi-modal large-scale datasets (c.g.. text-to-image or video datasets) remains an open challenge. Future research could investigate how to adapt blockwise modeling and semantic conditioning to settings that require more complex cross- modal reasoning and longer temporal consistency, such as text-driven video generation.
Non-uniform partitioning schedule. In this work, adopt uniform temporal segmentation strat- egy for simplicity. However, the generative trajectory exhibits varying complexity across timesteps, suggesting that certain regions (e.g., early noisy stages late refinement phases) may benefit from finer-grained modeling. Future work could explore non-uniform or learnable partitioning sched- ules that allocate computational resources adaptively based on local signal complexity, potentially improving both performance and efficiency.
F
Broader impact
The goal this work is to improve the efficiency and scalability of generative models. By introducing Blockwise Flow Matching (BFM), we reduce the computational burden of high-quality generation, making diffusion-based models more accessible for researchers and practitioners with limited re- sources. This has potential societal benefits in democratizing access to generative AI, enabling smaller labs, startups, and educational institutions to experiment with cutting-edge models without requiring extensive computational infrastructure. However, improved efficiency also lowers the barrier for misuse. Generative models can be exploited to produce content such as deepfakes or misinformation at scale. We acknowledge that its capabilities could be repurposed in harmful ways. Mitigating such misuse requires responsible downstream deployment, as well as efforts from the broader community to develop and enforce ethical standards around generative AI.
27

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Reviews:
[{"review_id": "6ZIGxiKbdQ", "reviewer": "Reviewer_ySpd", "summary": "The paper presents an interesting approach to flow-matching based methods by partitioning the generative trajectory into multiple temporal segments. Each segment is handled by a specialized smaller model for prediction. The proposed algorithm is called blockwise flow matching. Experimental results on ImageNet shows reasonable accelerations, like up to 4.9x over the baseline, without compromising the accuracy.", "questions": "The main questions are in the experimental section. Please well address the comments in the weakness section.", "limitations": "The paper does not explicitly provide the limitations of the proposed algorithm. Please reference the weakness section above for more details listed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "### Strengths\n- The idea of using blockwise flow matching is well motivated. As the paper claims, there are different characteristics for different timesteps during the flow trajectory. For example, early timesteps are dominated by irregular, low frequency patterns while the later timesteps require high-frequency details. Thus, using specialized models for different timesteps is reasonable.\n\n- The design of the proposed algorithm in Fig. 2 can well reduce the computation cost of the vanilla flow-matching based algorithm while maintaining feasible performance during the generation process.\n\n- The presentation of the paper is clear. The paper provides sufficient implementation details which are easy to reproduce the results.\n\n- The paper presents extensive ablation studies to validate the effectiveness of the proposed algorithm. \n\n\n### Weaknesses\n\n- Although the proposed algorithm reports reasonable speed up (based on FLOPs) as well as superior performance gain over the baseline, as shown in Table 2, blockwise flow matching actually increases the model parameters. Thus it will also consume more training memory, which makes the training cost larger than the vanilla flow matching algorithms. Besides, for the inference time, the decrease of FLOPs does not mean the model will have similar speed-up gain. Is it possible to provide the inference time cost for these algorithms reported in Table 2？\n\n- The proposed algorithm is based on ImageNet 256x256. How about the performance on the challenging text-to-image benchmark with larger generation size, like 1024x1024. Also, currently, the algorithm is based on the small model like SiT and REPA. Is it possible to be used in state-of-art image generation models?\n\n- For the performance evaluation, FID may not be consistent with human preference. Is it possible to provide a user-study to further validate the effectiveness of the proposed algorithm. \n\n- Is the proposed algorithm applicable to the algorithms with smaller diffusion steps, like 4-step model?", "was_revised": true, "final_justification": "Thanks for the authors' detailed rebuttal. Most of my concerns are cleared. I recommend borderline accept as the final rating.", "rebuttal": "Thank you for the valuable feedback. We'd like to clarify the additional questions the reviewer raised.\n\n---\n> ***Q1. Blockwise flow matching actually increases the model parameters. Thus, it will also consume more training memory, which makes the training cost larger than the vanilla flow matching algorithms.***\n\nOur Blockwise Flow Matching (BFM) can be viewed as sparse activation (a.k.a Mixture of Experts with a fixed router). Like MoEs, **our method increases parameters but maintains the computational cost/latency.** For comparison, we measured the training resource usage of BFM against strong baselines (SiT-XL/2, REPA-XL/2) on ImageNet 256×256, using 8 A100 GPUs with a batch size of 32 per GPU. As shown in the following table, **our model has the lowest GFLOPs and comparable GPU hours for training, while achieving the best FID score.** The quantitative results are as follows:\n| Model        | GFLOPs / Iteration | Train Hours (8*A100) | Memory (GB) | FID  | Params |\n|--------------|--------------------|--------------------|-------------|------|--------|\n| SiT-XL/2     | 22,789             | 53                 | 30          | 17.2 | 675M   |\n| REPA-XL/2    | 23,000             | 65                 | 31          | 7.9  | 675M   |\n| BFM-XL/2 (Ours)    | 21,816             | 57                 | 40          | 6.4  | 942M   |\n- **Training memory**: While BFM-XL/2 uses more parameters, the actual memory consumption is only moderately increased (from 30–31GB to 40GB), which remains practical for modern GPUs.\n- **Training efficiency**: The total training time is *comparable to or even less* than REPA-XL/2, and BFM achieves a substantially *better FID for the same number of iterations*.\nThese results show that, despite increased total parameter count, BFM **remains practical and scalable** for training, and delivers **improvements in sample quality**. Also, each block is assigned to a pre-defined time interval; therefore, it is possible to train each block parallelly (and separately) across multiple GPUs, which can further improve the training scalability.\nWe recognize this is a vital point for readers. We will add this table and a detailed discussion on the trade-offs between parameter count, training cost, and performance to the Appendix of our final paper.\n\n---\n> ***Q2. For the inference time, the decrease of FLOPs does not mean the model will have similar speed-up gain. Is it possible to provide the inference time cost?***\n\nWe thank the reviewer for this excellent point. We agree that theoretical FLOPs do not always translate to real-world speed-ups. To provide a concrete answer, we have benchmarked the wall-clock inference time of our models against the baselines on an A100 GPU with a batch size of 32. The results are summarized below:\n\n| Method                | NFE | wallclock run-time (s) | FLOPs (G) | FID  |\n|-----------------------|-----|-----------------------|-----------|------|\n| SiT-XL/2              | 246 | 51.21                 | 114.5     | 2.08 |\n| REPA-XL/2             | 246 | 51.21                 | 114.5     | 1.46 |\n| BFM-XL/2-SF (Ours)    | 246 | 47.96                 | 107.8     | 1.36 |\n| BFM-XL/2-SF-RA (Ours) | 246 | 19.42                 | 37.8      | 2.03 |\n\nThese empirical results confirm our method's efficiency:\n- Our primary model, BFM-SF is **7%** faster than the baselines while also achieving a superior FID score.\n- Our most efficient variant, BFM-SF-RA, achieves **63%** reduction in runtime while maintaining an FID score comparable to the SiT baseline.\n\nThis confirm that the observed drop in FLOPs with BFM is directly reflected in real-world speed-up, validating the practical efficiency of our approach. We will add this wall-clock time comparison to the main experimental section of our paper to demonstrate the practical efficiency of our method.\n\n---\n> ***Q3. How about the performance on the challenging text-to-image benchmark with larger generation size, like 1024x1024. Also, currently, the algorithm is based on the small model like SiT and REPA. Is it possible to be used in state-of-art image generation models?***\n\nWe thank the reviewer for these important questions on the scalability and generality of our method. While we have not yet run experiments on the billion-parameter models due to current resource constraints, our framework is fundamentally modular and can be integrated with larger, state-of-the-art backbones. To demonstrate scalability, we conducted two new experiments to address the reviewer's specific points:\n\n- **Scalability to Higher Resolution (ImageNet 512x512)**:\n\nTo test scalability, we trained BFM on ImageNet 512×512 for 400K iterations under identical settings. As shown below, our method outperforms strong baselines, demonstrating robust performance at higher resolutions.\n\n| Method         | FID    | NFE |\n|----------------|--------|-----|\n| SiT-S/4        | 102.54 | 246 |\n| REPA-S/4       | 91.34 | 246 |\n| BFM-S/4 (Ours) | 87.85  | 246 |\n\n- **Generalizing to Text-to-Image Backbone (MS-COCO 256x256)**:\n\nTo test generality, we integrated BFM into the state-of-the-art MMDiT [1] backbone for text-to-image synthesis. We trained on MS-COCO for 150K iterations (batch size 256), following the REPA setup. BFM again improves performance over both the original model and its REPA-augmented version.\n| Method         | FID  | NFE |\n|----------------|------|-----|\n| MMDiT          | 6.05 | 50  |\n| MMDiT + REPA   | 4.73 | 50  |\n| Ours (MMDiT + BFM)  | 4.32 | 48  |\n\nThese two results confirm that BFM is a versatile technique that scales effectively to higher resolutions and generalizes to improve state-of-the-art, multi-modal architectures for text-to-image generation.\n\n---\n\n> ***Q4. For the performance evaluation, FID may not be consistent with human preference. Is it possible to provide a user-study to further validate the effectiveness of the proposed algorithm.***\n\nWe fully agree that while FID is a widely used quantitative metric, it does not always align perfectly with human judgments of realism and visual preference. To provide a more comprehensive assessment, we have demonstrated additional quantitative metrics, *Inception Score, S-FID, Precision, and Recall* in the main paper, which measure different aspects of generation quality.\n\nIn response to your suggestion, we will consider including a user study where human evaluators perform blind, pairwise comparisons between our method's generations and those from the strongest baseline.\n\n> ***Q5. Is the proposed algorithm applicable to the algorithms with smaller diffusion steps, like 4-step model?***\n\nThank you for this insightful question that probes the generality of our method in the challenging few-step sampling regime.\nTo validate this, we integrated our method to the recently published MeanFlow [3] framework, an approach designed for training few-step diffusion model from scratch.\n\nSpecifically, we adapted our method by creating four specialist blocks for the 4-step diffusion trajectory and applying the MeanFlow objective to each. After training, we enable efficient sampling with only 4 steps (one per segment). The table below summarizes the results on ImageNet 256×256:\n\n|        Model        | NFE | FID  | \n|----------------|-----|------|\n| MeanFlow-B/2   | 4   | 13.2 |\n| Ours (MeanFlow-B/2+BFM)\t | 4   | 9.7 |\n\n As shown, BFM achieves significantly better FID. This experiment confirms that BFM is not only compatible with few-step frameworks but provides a significant performance advantage. \n\nGiven the strength of this result, we will add this experiment in the revised manuscript to highlight BFM's applicability to the few-step generation setting.\n\n---\n[1] Esser, Patrick, et al. \"Scaling rectified flow transformers for high-resolution image synthesis.\" Forty-first international conference on machine learning. 2024 \\\n[2] Radford, Alec, et al. \"Learning transferable visual models from natural language supervision.\" International conference on machine learning. PmLR, 2021 \\\n[3] Geng, Zhengyang, et al. \"Mean flows for one-step generative modeling.\" arXiv preprint arXiv:2505.13447 (2025)"}, {"review_id": "co1RgyuUot", "reviewer": "Reviewer_ByUL", "summary": "This paper introduces Blockwise Flow Matching (BFM), a novel framework to address the efficiency and performance limitations of Flow Matching models. It partitions the generative trajectory into segments, each handled by a smaller, specialized network block to improve both modeling accuracy and inference speed. Furthermore, by incorporating semantic guidance and an efficient feature approximation strategy, the method achieves both quality and speed improvement. Overall, this paper proposes a brand new paradigm for Flow Matching models.", "questions": "1. In Equation 7, the authors supervise the denoising process by velocity within the $m$-th segment. I wonder whether supervising by velocity to $x_1$, namely, $\\frac{x_{t_m}-x_1}{t_m-1}$ will result in performance degradation.\n2. It is suggested to provide an ablation study where the feature alignment network is trained without the $\\mathcal{L}_{align}$, which demonstrates the benefits of explicitly aligning to pretrained representations.\n3. In Section 4.2 (Line 163), the authors mention that BFM can take various additional conditions as inputs (e.g., class labels or text prompts). However, I only see class-label-conditioned generation in the paper. Can the authors provide analysis regarding text-conditioned generation?\n4. The design of the Semantic Feature Guidance module is similar to recent work DDT [1]. The authors are advised to add a citation and discussion. \n5. It would be better if the authors provided a discussion or visualization of typical failure cases to demonstrate the limitations of BFM.\n\n[1] Wang, Shuai, et al. \"Ddt: Decoupled diffusion transformer.\" arXiv preprint arXiv:2504.05741 (2025).", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The main idea of this paper, partitioning the generative trajectory into segments handled by specialized, smaller blocks, is a novel design and effectively deals with the temporal heterogeneity of the generation process. \n2. The experiments are rigorous, comprehensive, and conducted on a competitive benchmark (ImageNet 256x256). The detailed ablation studies and visualizations systematically validate the contribution of each component of the proposed method, demonstrating high-quality research practice.\n3. This is a well-organized paper. The authors do an excellent job of motivating the problem, explaining their method, and presenting their results in an accessible manner.\n\nWeaknesses\n1. Some key experiments validating the effectiveness of the proposed modules are missing, which I elaborate on in my Questions.", "was_revised": true, "final_justification": "I thank the author for patiently addressing my questions, and I have decided to improve my score.", "rebuttal": "Thank you for the valuable feedback. We'd like to clarify the additional questions the reviewer raised.\n\n---\n\n> ***Q1. In Equation 7, the authors supervise the denoising process by velocity within the m-th segment. I wonder whether supervising by velocity to $x_1$, namely, $({x_{t_m} - x_1})/({t_m - 1})$ will result in performance degradation.***\n\nWe thank the reviewer for this insightful question about the formulation of our objective. The two supervision targets are, in fact, mathematically identical. From the equations (4) and (5) in our paper, the endpoints $x_{t_{m-1}}$ and $x_{t_m}$ are defined as linear interpolations between $x_0$ and $x_1$:\n\n$$\nx_{t_{m-1}} = (1-t_{m-1})x_0 + t_{m-1}x_1, \\quad x_{t_m} = (1-t_{m})x_0 + t_{m}x_1.\n$$\n\nTherefore,\n$$\n\\frac{x_{t_m} - x_{t_{m-1}}}{t_m - t_{m-1}} = \\frac{[(1-t_{m})x_0 + t_{m}x_1] - [(1-t_{m-1})x_0 + t_{m-1}x_1]}{t_m - t_{m-1}}\n$$\n$$\n= \\frac{(t_{m-1}-t_m)x_0 + (t_m - t_{m-1})x_1}{t_m - t_{m-1}} = -x_0 + x_1 = x_1 - x_0.\n$$\n\nSimilarly,\n$$\n\\frac{x_{t_m} - x_1}{t_m - 1} = \\frac{[(1-t_{m})x_0 + t_{m}x_1] - x_1}{t_m - 1} = \\frac{(1-t_m)x_0 + (t_m-1)x_1}{t_m - 1} = x_1 - x_0.\n$$\n\nTherefore, there is no performance difference because the supervision signal is identical in both cases. We chose our formulation for notational consistency within the block-wise framework.\n\n---\n\n> ***Q2. It is suggested to provide an ablation study where the feature alignment network is trained without the alignment loss, which demonstrates the benefits of explicitly aligning to pretrained representations.***\n\nWe thank the reviewer for this excellent suggestion to empirically validate our design. As requested, we conducted an ablation study where the feature alignment network was trained without the alignment loss, on ImageNet 256x256 for 100K iterations:\n\n| Method     | Alignment loss | FID  |\n|------------|---------------|------|\n| BFM-S/2    | x             | 73.5 |\n| BFM-S/2    | o             | 66.9 |\n\nAs shown, removing the alignment loss results in a substantial drop in sample quality (6.6 FID points), clearly demonstrating the effectiveness of explicit alignment to pretrained representations. \n\nWe will add this ablation study to the Experiments section of our revised manuscript to quantitatively demonstrate the importance of the alignment loss.\n\n---\n\n> ***Q3. Can the authors provide analysis regarding text-conditioned generation?***\n\nWe thank the reviewer for this important question. To demonstrate our method's effectiveness on text-conditioned generation, we integrated BFM into the state-of-the-art MMDiT [1] backbone and trained it on the MS-COCO benchmark for 150K iterations (batch size 256), following the REPA setup. While testing on billion-scale models remains future work, this experiment shows BFM's compatibility with and ability to improve a modern, multi-modal architecture.\n\n| Method         | FID  | NFE |\n|----------------|------|-----|\n| MMDiT          | 6.05 | 50  |\n| MMDiT + REPA   | 4.73 | 50  |\n| Ours (MMDiT + BFM)  | 4.32 | 48  |\n\nAs the results show, our BFM-augmented model surpasses both the original MMDiT and the REPA-enhanced version, achieving a stronger FID score. These results confirm that BFM is robust and adaptable to modern transformer-based multi-modal architectures. \n\n---\n\n> ***Q4. The design of the Semantic Feature Guidance module is similar to recent work DDT [2]. The authors are advised to add a citation and discussion.***\n\nWe thank the reviewer for pointing out this highly relevant concurrent work. We agree that DDT shares the high-level principle of using an explicit alignment module to guide generation.\nOur key distinction lies in the architectural integration and purpose. While DDT applies guidance to a standard diffusion model, our Semantic Feature Guidance is a core component of our modular, blockwise flow matching framework. It specifically provides high-level conditioning to a set of specialized, time-step-dependent velocity networks.\n\nWe will update our Related Work section to include a citation and a detailed discussion of DDT. We will clarify the conceptual similarities while also highlighting the unique architectural differences of our approach.\n\n---\n\n> ***Q5. It would be better if the authors provided a discussion or visualization of typical failure cases to demonstrate the limitations of BFM.***\n\nThank you for this valuable suggestion. While our method significantly improves on baselines, it can still produce failure cases (e.g., minor artifacts or implausible object structures) that are common to most generative models trained on complex datasets like ImageNet. We have not observed failure modes that are uniquely attributable to our blockwise design or semantic guidance.\n\nWe will include a curated set of generated images that exhibit typical failure modes and discuss them in the context of general challenges in generative modeling.\n\n---\n[1] Esser, Patrick, et al. \"Scaling rectified flow transformers for high-resolution image synthesis.\" Forty-first international conference on machine learning. 2024 \\\n[2] Wang, Shuai, et al. \"Ddt: Decoupled diffusion transformer.\" arXiv preprint arXiv:2504.05741 (2025)."}, {"review_id": "5zhUhCY84C", "reviewer": "Reviewer_5kd7", "summary": "The paper proposes partitioning the original diffusion process into multiple time intervals, where each interval is managed by a separate, compact network. This design reduces the model feedforward cost incurred at every evaluation step.", "questions": "Q1. Why FRN is needed? Why is not not trained jointly with feature alignment network?\n\nQ2. Using non-overlapping time interval is reasonable since it is easier to manage. However, it also has a limitation that there is a disconnected information at the starting and ending point between each interval. Have the authors considered this issue in the method? \n\nQ3. In semantic feature guidance, what is the model performance when only aligment loss is used and no conditioning semantic feature $f_t$ is used. This allows to compare with the naive REPA baseline.\n\nQ4. As concern in Q2, this seems that the authors addressed a different issue via Feature Residual Approximation which is the consistency of starting point and intermediate point within the same interval. However, there is an inevitable discrepancy between the ending point of the previous time interval and the starting point of the next time interval, even though they should theoretically be identical. The feature residual only addresses the discrepancy of within-interval features, not the temporal discontinuity between consecutive intervals.\n\nQ5. Have the authors tried a simple baseline that aligns the features of velocity block with pretrained features, without the presence of Semantic module? This is similar to REPA method.\n\nQ6. Feature residual approximation is just one approach. Have the authors tried a simple interpolation between the start and end points instead so there is no need of additional learnt module.", "limitations": "yes but please also address the concern of discontinuity of non-overalaping inverals above.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strenths:\n- Decomposing a cumbersome network into multiple smaller ones is a sensible idea where each handles an assigned temporal block.  \n- This gives a flexibility in eliminating computational cost while obtaining good generation quality.\n- The exposition is clear and well-motivated.\n\nWeaknesses:\n- The proposed components, including semantic guidance and the feature residual module, add considerable complexity to the method and could benefit from clearer motivation to justify their inclusion.\n- There is a compromise of model performance when using the Feature Residual Approximation which is understandable. I would be helpful to include a speed vs. FID chart for demonstration of the tradeup.", "was_revised": true, "final_justification": "The rebuttal and follow-up response from the authors generally addressed my major concerns about the discontinuity between adjacent segments. So, I raised my score to reflect this. The paper's contribution is substantial with strong performance advantage (both speed and quality) which could facilitate for the next AI generation models.", "rebuttal": "Thank you for the valuable feedback. We'd like to clarify the additional questions the reviewer raised.\n\n---\n\n> ***Q1. The proposed components, including semantic guidance and the feature residual module, add considerable complexity to the method and could benefit from clearer motivation to justify their inclusion. Why FRN is not not trained jointly with feature alignment network?***\n\nWe thank the reviewer for asking for a clearer justification of our design choices.\nWe have provided a detailed motivation in Sections 4.2–4.3 and Table 1 in the main paper, but we are happy to clarify here:\n\nOur two main components are designed to solve specific, practical challenges in the blockwise modeling framework.\n- **Semantic Feature Guidance**: The velocity blocks operating at early timesteps primarily encounter highly noisy samples, limiting their ability to learn high-level semantic structure from clean data. Our solution is a shared alignment network that provides a consistent, global semantic understanding to all blocks. This encourages *smooth transitions and rich semantic guidance* throughout the diffusion process.\nMoreover, this module adds minimal complexity by following an encoder–decoder structure widely used in modern architectures.\n\n- **Feature Residual Network**: The problem is that repeatedly running the large guidance network during inference is inefficient. Our solution is the FRN, a very lightweight network that learns to approximate the guidance features locally within each block. This eliminates the need to call the alignment network at every inference step. FRN is a lightweight, optional module: BFM with semantic feature guidance alone is already powerful for high-fidelity generation, and FRN simply provides an efficient pathway for inference when computational resources are constrained.\n\n- **Why not train jointly?** If trained together, the shared alignment network might learn features that are easier for the FRN to approximate, rather than learning the best possible features for guiding generation. By using a two-stage process, we first train the guidance network to be as powerful as possible without constraints. Then, in a second stage, we train the lightweight FRN to mimic this optimal. We found empirically that this staged approach leads to more stable training and higher final sample quality.\n\nIn summary, both the semantic feature guidance module and FRN address concrete challenges in blockwise flow modeling, ensuring global semantic coherence and practical inference efficiency.\n\n---\n\n> ***Q2. Using non-overlapping time interval is reasonable since it is easier to manage. However, it also has a limitation that there is a disconnected information at the starting and ending point between each interval. Have the authors considered this issue in the method?***\n\nWe thank the reviewer for this insightful question about potential discontinuities at our block boundaries. \nOur design includes two mechanisms that inherently mitigate this issue:\n- Our framework is designed so that the marginal distributions at the endpoint of one segment and the starting point of the next segment are matched exactly. This theoretically prevents any explicit discontinuity in the underlying probability trajectory.\n- Furthermore, our alignment network is shared across all segments and learns features over the entire diffusion process, which encourages smooth transitions and consistency between blocks. \n\nEmpirically, we have not observed any visual artifacts or performance degradation that could be attributed to boundary discontinuities, which we believe is due to these two design choices.\n\nWe acknowledge the possibility of subtle transitions at segment boundaries. In future work, we plan to explore mechanisms to further encourage temporal continuity between blocks, such as overlapping temporal segments.\n\n---\n\n> ***Q3. In semantic feature guidance, what is the model performance when only aligment loss is used and no conditioning semantic feature is used. This allows to compare with the naive REPA baseline.***\n\nWe thank the reviewer for this excellent suggestion, which helps to isolate the specific contribution of our blockwise architecture. As requested, we ran an experiment using BFM but replaced our explicit guidance module with REPA-style alignment loss, using DINOv2 as the target. This provides a direct comparison to a standard Flow Matching (FM) model with REPA.\n\n|               | FID   |\n|---------------|-------|\n| FM + REPA      | 72.9  |\n| BFM + REPA      | 70.23 |\n\nThe results show that even without our proposed semantic conditioning, the blockwise architecture itself provides a clear performance improvement over the standard baseline. This demonstrates the inherent benefit of using specialized temporal blocks. We will include and clarify these results in the revised manuscript.\n\n---\n\n> ***Q4. As concern in Q2, this seems that the authors addressed a different issue via Feature Residual Approximation which is the consistency of starting point and intermediate point within the same interval. However, there is an inevitable discrepancy between the ending point of the previous time interval and the starting point of the next time interval, even though they should theoretically be identical. The feature residual only addresses the discrepancy of within-interval features, not the temporal discontinuity between consecutive intervals.***\n\nWe thank the reviewer for this follow-up question. We would like to clarify that the Feature Residual Network (FRN) is *not* introduced to address the consistency between the starting and intermediate points within the same interval. Instead, its primary purpose is to enable efficient inference by approximating the output of the alignment network, thus reducing computational overhead at test time.\n\nThe issue of continuity between blocks is handled by two other core design choices, as mentioned in Q2: 1) \nshared alignment network, and 2) identical marginal distribution at boundaries.\n\n---\n\n> ***Q5. Have the authors tried a simple baseline that aligns the features of velocity block with pretrained features, without the presence of Semantic module? This is similar to REPA method.***\n\nThank you for your question. This is a crucial ablation that we also addressed in our response to Q3 above. As described in our previous answer, we have ablated the semantic module and evaluated the performance of BFM when using only the REPA-style alignment loss, directly aligning velocity block features with pretrained features.\n\n---\n\n> ***Q6. Feature residual approximation is just one approach. Have the authors tried a simple interpolation between the start and end points instead so there is no need of additional learnt module.***\n\nThank you the insightful suggestion. While interpolating between the start and end points of each interval is an appealing and efficient idea, it is unfortunately not feasible during inference: the end point of the interval corresponds to a future state, which is precisely what the model is tasked with generating. As a result, we cannot access this information during sampling.\n\nThis is precisely why our Feature Residual Network (FRN) is necessary. Instead of interpolating between two known points, the FRN acts as a feature predictor, conditioned only on the information available up to the current step. This enables efficient and accurate inference without requiring knowledge of future states."}, {"review_id": "mXJLG7uvgR", "reviewer": "Reviewer_wHnp", "summary": "The authors of this work study a novel training scheme for flow matching models, which are state-of-the-art in image, text, etc, generation. In standard flow matching training, the practitioner has access to the start and end distributions and trains a neural network to learn vector fields at random times within the interval [0,1]. The hardest part in training is being able to capture the precise moments where the feature-learning takes place, and at inference, the need to discretize the flow into many steps is also expensive. To remedy these issues, this work proposes BlockwiseFlowMatching (BFM), where they train more (but smaller) specialized velocity blocks for particular time intervals. They compare their approach to several other works and they achieve SOTA results on large imagenet datasets.", "questions": "- Is it possible to distill the training ideas into a few key steps in the main text? I personally found Figure 2 and the accompanying caption very difficult to understand compared to the pseudocode in the appendix\n- Do you attempt to see what happens when you take other paths?\n- Following the \"strengths\" comment above, if they are available, is it possible to see what the images look like for various times (apart from just the semantic features)?\n- From the semantic features: why does it look like the model very early on learns the image? This is a bit strange?\n- Is Table1 inconsistent with the \"lower is better\"? I feel like it would be better if the first column said something like 0.66 and 1/1.09, and so on", "limitations": "N/A", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "A huge strength of this paper lies in its simplicity---the idea is very natural from an algorithmic/training perspective. My understanding is that many folks have tried to basically over- or under-tune training via stepsize schedulers, and I view this work as a complementary perspective on the matter (namely, to segment the time interval and train in block instead). I really appreciated the figures in the main text and appendix that highlight the \"semantic features over timesteps\"---this was very cool.\n\nA weakness is that the work is purely empirical, but that is less of a weakness and more of just where the paper fits in the ML space. The clarity could be improved in some cases; see below. I am also not an expert, but it is not clear to me whether or not their experimentation is exhaustive enough with respect to the existing literature. Looking closer at Table 2, the number of parameters required is sometimes larger than other models (see e.g., the reference [45]) with comparable FID and the number of FLOPs is lower. \n\nThe numerical results are not entirely compelling and seem a bit catered for the datasets in question. That being said, I do appreciate the novelty this idea brings to this space, and I thus recommend weak accept.", "was_revised": true, "final_justification": "All of my initial comments were addressed", "rebuttal": "Thank you for the valuable feedback. We'd like to clarify the additional questions the reviewer raised.\n\n---\n\n> ***Q1. It is not clear to me whether or not their experimentation is exhaustive enough with respect to the existing literature. The numerical results are not entirely compelling and seem a bit catered for the datasets.***\n\nWe appreciate the reviewer for the concern about the scope of experiments. Our primary experiments were conducted on ImageNet to enable rigorous benchmarking and direct comparison with recent diffusion and flow models. To address the concern that our results are catered, we have conducted two significant new experiments on more demanding tasks beyond the initial ImageNet 256x256 benchmark.\n\n- **Scaling to Higher Resolution (ImageNet 512x512)**:\n\nTo prove our method isn't just strong for moderate resolution, we tested it on higher-resolution 512x512 image generation. The results show a compelling and significant improvement over strong baselines.\n\n| Method         | FID    | NFE |\n|----------------|--------|-----|\n| SiT-S/4        | 102.54 | 246 |\n| REPA-S/4       | 91.34 | 246 |\n| BFM-S/4 (Ours) | 87.85  | 246 |\n\nOur method achieves over 3 FID improvement over the next best baseline, demonstrating strong performance and scalability.\n\n- **Generalizing to Text-to-Image Synthesis (MS-COCO)**:\n\nTo prove our method's general applicability beyond class-conditional generation, we integrated it into a state-of-the-art text-to-image backbone (MMDiT [1]) and tested it on the MS-COCO dataset.\n\n| Method         | FID  | NFE |\n|----------------|------|-----|\n| MMDiT          | 6.05 | 50  |\n| MMDiT + REPA   | 4.73 | 50  |\n| Ours (MMDiT + BFM)  | 4.32 | 48  |\n\nThese results confirm that BFM scales robustly to higher resolutions and adapts seamlessly to modern, multi-modal transformer architectures. Although we have not yet conducted experiments at the largest model scales due to hardware limits, these results demonstrate that our framework is fundamentally modular and can be integrated with larger, state-of-the-art backbones.\n\n---\n\n> ***Q2. Is it possible to distill the training ideas into a few key steps in the main text? I personally found Figure 2 and the accompanying caption very difficult to understand compared to the pseudocode in the appendix.***\n\nThank you for your helpful feedback regarding the clarity of Figure 2 and the training procedure. In the revised version, we will summarize the training pipeline in the main text as a concise list of key steps and revise Figure 2 and its caption for greater clarity. We will also directly reference the pseudocode in the appendix for readers seeking more detailed implementation guidance.\n\n---\n\n> ***Q3. Do you attempt to see what happens when you take other paths?***\n\nThank you for this excellent question. We interpret \"other paths\" as referring to different probability trajectories between noise and data (e.g., non-linear paths vs. our default linear one). To test this, we applied our BFM framework to a DiT model that uses the standard DDPM path. The results clearly show that our method provides a significant benefit even when applied to this different, non-linear trajectory. The results are summarized below:\n\n| Method              | FID  |\n|---------------------|------|\n| DiT-S/2 (DDPM)      | 90.4 |\n| BFM-S/2 (DDPM)      | 77.2 |\n\nThis 13.2-point FID improvement demonstrates that the benefits of our method are robust and not limited to a specific type of probability path.\n\n---\n\n> ***Q4.  If they are available, is it possible to see what the images look like for various times (apart from just the semantic features)?***\n\nWe thank the reviewer for this excellent suggestion. Visualizing the generated images at various timesteps along the diffusion trajectory can provide valuable insight into how BFM operates and how different blocks contribute to the final sample. In the revision, we will include visualizations of intermediate generations at multiple timesteps.\n\n---\n> ***Q5. From the semantic features: why does it look like the model very early on learns the image? This is a bit strange?***\n\nThis is an insightful observation that highlights a key feature of our semantic feature. Our alignment network learns to predict the final image's semantic features very early on, even from highly noisy inputs. This is the intended behavior and a core strength of our design. \n\nOur alignment network is explicitly trained to match the features of the clean image regardless of the input timestep, which learns to be a powerful semantic denoiser. As a result, the network learns to robustly extract semantic information from noisy images. This provides a strong, consistent semantic feature that guides all the specialized velocity blocks throughout the entire generation process, which we believe is a primary reason for our method's strong performance. \n\nWe acknowledge this is an interesting phenomenon and will discuss it in the revised manuscript.\n\n---\n\n> ***Q6. Is Table1 inconsistent with the \"lower is better\"? I feel like it would be better if the first column said something like 0.66 and 1/1.09, and so on.***\n\nThank you for your suggestion regarding the presentation of Table 1. We structured Table 1 to follow the logical flow of our method section—first introducing blockwise flow matching, then semantic feature guidance, and finally the feature approximation network—so that the progression of methods aligns with the corresponding impact on fidelity and efficiency.\n\nHowever, we appreciate your feedback on clarity. In the revised version, we will consider reformatting Table 1 to make the “lower is better” interpretation more transparent (for example, by using relative ratios such as 0.66 or 1/1.09) as you suggested. Thank you for helping us improve the presentation of our results.\n\n---\n\n[1] Esser, Patrick, et al. \"Scaling rectified flow transformers for high-resolution image synthesis.\" Forty-first international conference on machine learning. 2024 \\"}, {"review_id": "mqn6mLGoKL", "reviewer": "Reviewer_6WUg", "summary": "This paper introduces Blockwise Flow Matching (BFM), a method that splits the generative trajectory in flow matching models into multiple temporal “blocks,” each with their own smaller, specialized network for a subset of timesteps. Combined with a Semantic Feature Guidance module (using pretrained DINOv2 features) and a lightweight Feature Residual Approximation for fast inference, BFM aims to improve both sample quality and efficiency. Experiments on ImageNet 256x256 show state-of-the-art FID at significantly reduced FLOPs, suggesting BFM dramatically pushes the quality/speed Pareto frontier.", "questions": "**Questions** \n\n- In line 138, are the intervals uniform? Could the optimal non-uniform intervals in [2] provide any motivation or benefits to your design?\n\n**References**\n\n[1] Yan, Hanshu, et al. \"Perflow: Piecewise rectified flow as universal plug-and-play accelerator.\" arXiv preprint arXiv:2405.07510 (2024).\n\n[2] Nguyen, Bao, Binh Nguyen, and Viet Anh Nguyen. \"Bellman optimal stepsize straightening of flow-matching models.\" arXiv preprint arXiv:2312.16414 (2023).\n\n[3] Yoon, Jongmin, and Juho Lee. \"Sequential Flow Straightening for Generative Modeling.\" arXiv preprint arXiv:2402.06461 (2024).", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n- The paper is clear and easy to follow.\n- Integrating pretrained semantic features makes sense and performs better than previous representation alignment techniques.\n- Demonstrates robust improvements across quality and FLOPs, backed by systematic ablations.\n\n**Weaknesses**\n\n- I questioned the novelty of the BFM. Previous works have already divided the entire time interval into multiple segments and then optimized the inference quality for each of them. Some mentioned works can be listed as [1], [2], [3]. For example, the work [2] uses a similar loss function to yours; the difference is that they use only one network, which is specialized for all sub-segments. Similar principles can be found in [2] and [3]. I believed that deploying one neural network for inference is much resource-friendly than the paper’s approach. Could a distilled single model recover BFM’s benefits?\n\n- The comparison with the works mentioned in the first drawback is highly recommended.\n- Results are limited to ImageNet and strong pretrained image encoders; adaptation to other data types or domains isn’t addressed.\n- Increased total parameters from block specialization may strain memory and training scalability, not fully discussed.\n- The choice and allocation of temporal blocks lacks theory or automation—performance appears sensitive to segmentation hyperparameters.", "was_revised": true, "final_justification": "The author addresses my concern about the novelty of the paper. I decided to raise the score", "rebuttal": "Thank you for the valuable feedback. We'd like to clarify the additional questions the reviewer raised.\n\n---\n> ***Q1. The comparison with the relevant distillation-based methods [1,2,3] that aim to optimize the temporal steps.***\n\nWe thank the reviewer for referring interesting works. We will include them in the final version with the discussion below. \n\nOur framework, Blockwise Flow Matching (BFM), is a **new architecture that can be trained from scratch.** In our experiment, we trained BFM from scratch. For more efficient and effective from-scratch training, we proposed a **new alignment method, SemFeat, tailored for BFM, using DINOv2**. To some extent, this is relevant to the prior works [1,2,3], but our framework does **NOT** leverage any pre-trained diffusion models. \nIndeed, **our approach is orthogonal and complementary to distillation-based methods.** Distillation aims to reduce the “number of sampling steps”, whereas BFM is focused on reducing the “computation cost per step” via architectural specialization. Importantly, distillation or schedule-optimization techniques can be incorporated into BFM to further accelerate inference if desired. Thus, BFM can serve as a strong foundation that benefits from further post-training improvements.\n\nTo directly demonstrate BFM's *from-scratch* efficiency, we integrated our method into the recently published MeanFlow framework [4], which enables few-step sampling from scratch. Specifically, we adapted our method by creating four specialist blocks for the 4-step diffusion trajectory and applying the MeanFlow objective to each segment. After training, we can efficiently sample with only 4 steps (one per segment). The table below summarizes the results on ImageNet 256×256.\n\n| Model                   | NFE | FID  |\n|-------------------------|-----|------|\n| MeanFlow-B/2            | 4   | 13.2 |\n| Ours (MeanFlow-B/2+BFM) | 4   | 9.7  |\n\nThis FID improvement confirms that BFM provides substantial gains as a from-scratch few-step methodology, independent of any distillation techniques.\n\nThat said, we also recognize the importance of including relevant papers to provide more comprehensive understanding of the paper. We will cite the papers and include discussion in the revised manuscript.\n\n---\n\n> ***Q2. Results are limited to ImageNet and strong pretrained image encoders; adaptation to other data types or domains isn’t addressed.***\n\nThank you for this excellent point about the generality of our method. While our initial experiments focused on ImageNet for rigorous benchmarking, our framework is not limited to this setting. To demonstrate its versatility, we have conducted two significant new experiments.\n\n- **Scalability to Higher Resolution (ImageNet 512x512)**:\n\nTo test scalability, we trained BFM on ImageNet 512×512 for 400K iterations under identical settings. As shown below, our method outperforms strong baselines, demonstrating robust performance at higher resolutions.\n\n| Method         | FID    | NFE |\n|----------------|--------|-----|\n| SiT-S/4        | 102.54 | 246 |\n| REPA-S/4       | 91.34 | 246 |\n| BFM-S/4 (Ours) | 87.85  | 246 |\n\n- **Generalizing to Text-to-Image Backbone (MS-COCO 256x256)**:\n\nTo test generality, we integrated BFM into the state-of-the-art MMDiT [1] backbone for text-to-image synthesis. We trained on MS-COCO for 150K iterations (batch size 256), following the REPA setup. BFM again improves performance over both the original SOTA model and its REPA-augmented version.\n| Method         | FID  | NFE |\n|----------------|------|-----|\n| MMDiT          | 6.05 | 50  |\n| MMDiT + REPA   | 4.73 | 50  |\n| Ours (MMDiT + BFM)  | 4.32 | 48  |\n\nThese two results confirm that BFM is a versatile technique that scales effectively to higher resolutions and generalizes to improve state-of-the-art, multi-modal architectures for text-to-image generation.\n\n---\n\n> ***Q3. Increased total parameters from block specialization may strain memory and training scalability, not fully discussed.***\n\nOur Blockwise Flow Matching (BFM) can be viewed as sparse activation (a.k.a Mixture of Experts with a fixed router). Like MoEs, **our method increases parameters but maintains the computational cost/latency.** For comparison, we measured the training resource usage of BFM against strong baselines (SiT-XL/2, REPA-XL/2) on ImageNet 256×256, using 8 A100 GPUs with a batch size of 32 per GPU. As shown in the following table, **our model has the lowest GFLOPs and comparable GPU hours for training, while achieving the best FID score.** The quantitative results are as follows:\n| Model        | GFLOPs / Iteration | Train Hours (8*A100) | Memory (GB) | FID  | Params |\n|--------------|--------------------|--------------------|-------------|------|--------|\n| SiT-XL/2     | 22,789             | 53                 | 30          | 17.2 | 675M   |\n| REPA-XL/2    | 23,000             | 65                 | 31          | 7.9  | 675M   |\n| BFM-XL/2 (Ours)    | 21,816             | 57                 | 40          | 6.4  | 942M   |\n- **Training memory**: While BFM-XL/2 uses more parameters, the actual memory consumption is only moderately increased (from 30–31GB to 40GB), which remains practical for modern GPUs.\n- **Training efficiency**: The total training time is *comparable to or even less* than REPA-XL/2, and BFM achieves a substantially *better FID for the same number of iterations*.\nThese results show that, despite increased total parameter count, BFM **remains practical and scalable** for training, and delivers **improvements in sample quality**. Also, each block is assigned to a pre-defined time interval; therefore, it is possible to train each block parallelly (and separately) across multiple GPUs, which can further improve the training scalability.\nWe recognize this is a vital point for readers. We will add this table and a detailed discussion on the trade-offs between parameter count, training cost, and performance to the Appendix of our final paper.\n---\n\n> ***Q4. The choice and allocation of temporal blocks lacks theory or automation—performance appears sensitive to segmentation hyperparameters.***\n\nThis is an excellent point which is an interesting future direction, as discussed in \"Limitation and Future work\" section of our paper.\nTable 4 in our main paper shows that performance generally improves as the number of blocks increases. However, it leads to a larger model size. We empirically chose the number of temporal blocks based on the trade-off between performance and model size, but we agree that exploring a more theoretically-grounded or automated way to determine the optimal block segmentation is a promising direction for future research.\n\n---\n\n> ***Q5. In line 138, are the intervals uniform? Could the optimal non-uniform intervals in [2] provide any motivation or benefits to your design?***\n\nYes, in our current work, the time intervals are uniform. We chose this simple approach to provide a clean condition for our core contributions: the blockwise architecture and the semantic guidance module.\n\nWe appreciate the reviewer's insightful suggestion. Using optimal non-uniform intervals, like those discussed in [2], is a fantastic idea and a natural next step for our framework. As we discussed in Limitation and Future work section, dynamically allocating more capacity (i.e., more or wider blocks) to more \"difficult\" parts of the generation trajectory could lead to significant further improvements in efficiency and quality.\n\n---\n[1] Yan, Hanshu, et al. \"Perflow: Piecewise rectified flow as universal plug-and-play accelerator.\" arXiv preprint arXiv:2405.07510 (2024). \\\n[2] Nguyen, Bao, Binh Nguyen, and Viet Anh Nguyen. \"Bellman optimal stepsize straightening of flow-matching models.\" arXiv preprint arXiv:2312.16414 (2023). \\\n[3] Yoon, Jongmin, and Juho Lee. \"Sequential Flow Straightening for Generative Modeling.\" arXiv preprint arXiv:2402.06461 (2024). \\\n[4] Geng, Zhengyang, et al. \"Mean flows for one-step generative modeling.\" arXiv preprint arXiv:2505.13447 (2025)."}]

Author rebuttal:

Meta-review: This paper proposes Blockwise Flow Matching (BFM), a new framework for flow matching generative models. Instead of a single large network handling the entire generative trajectory, BFM partitions the trajectory into temporal segments, each handled by a specialized smaller “velocity block.” To enhance quality and efficiency, the authors also introduce two components: (1) Semantic Feature Guidance, which conditions velocity blocks on semantically rich pretrained representations (DINOv2), and (2) Feature Residual Approximation (FRA), which approximates semantic features to reduce inference cost. Extensive experiments on ImageNet 256×256 demonstrate substantial Pareto improvements in FID vs. FLOPs, with additional results on higher-resolution (512×512) and text-to-image (MS-COCO) benchmarks showing scalability and generality.

All five reviewers viewed the paper as technically solid, with contributions that improve both efficiency and sample quality in flow matching models. Several reviewers (ByUL, 5kd7, 6WUg, wHnp) explicitly raised their scores after rebuttal clarifications and new results. While concerns remain about increased parameters, clarity of exposition, and novelty relative to prior step-size/dynamic scheduling works, the rebuttal convincingly positioned BFM as a distinct and complementary architectural innovation, which supports the decision of acceptance.
Decision: Accept (poster)