In this paper, we present Laplacian multiscale flow matching (LapFlow), a novel framework that enhances flow matching by leveraging multi-scale representations for image generative modeling. Our approach decomposes images into Laplacian pyramid residuals and processes different scales in parallel through a mixture-of-transformers (MoT) architecture with causal attention mechanisms. Unlike previous cascaded approaches that require explicit renoising between scales, our model generates multi-scale representations in parallel, eliminating the need for bridging processes. The proposed multi-scale architecture not only improves generation quality but also accelerates the sampling process and promotes scaling flow matching methods. Through extensive experimentation on CelebA-HQ and ImageNet, we demonstrate that our method achieves superior sample quality with fewer GFLOPs and faster inference compared to single-scale and multi-scale flow matching baselines. The proposed model scales effectively to high-resolution generation (up to 1024×1024) while maintaining lower computational overhead.
Figures & tables
Figure 1: Multi-scale generation process of our model . The proposed model follows a coarse-to-fine generation strategy across scales in a Laplacian pyramid. This figure demonstrates a three-level version of ours, where T2 , T1 are two critical points defining three sampling segments for three scales. Starting from a random noise at t=0 , our model first denoises the coarsest scale until t=T2 , then progressively conditions finer scales on completed coarser scales ( t=T2 to T1 and t=T1 to 1 ). This causal structure ensures coherent image generation by maintaining hierarchical dependencies across scales, ultimately producing high-fidelity samples with both global consistency and fine details.
Figure 2: ( Left: ) Schematic of the LapFlow model Vθ . The multi-scale transformer takes multi-scale noisy states as input, conditioned on time and label, and predicts velocities for each input scale. While the model can take an arbitrary number of scales as input, we show two here for simplicity. ( Middle: ) Details of one multi-scale MoT block. We use separate QKVs for different scales, while the attention is computed globally. Furthermore, we adopt a mask to enforce causal relationships across scales. ( Right: ) Details of scale-specific PreAttnMod and PostAttnMod modules ( Peebles and Xie, 2023 ) , where each PostAttnMod module includes a feedforward network (FFN).
Methods
Backbone
Resolution
Space
FID ↓
Recall ↑
NFE
Time (s)
Params
GFLOPs
Standard Resolution (256)
FM ( Lipman et al., 2023 )
U-Net
256×256
Image
7.34
-
128
-
-
-
LDM ( Rombach et al., 2022 )
U-Net
256×256
Latent
5.11
0.49
50
2.90
150M
10.2
LFM ( Dao et al., 2023 )
DiT-L/2
256×256
Latent
5.26
0.46
89
1.70
541M
22.1
Pyramidal Flow ( Jin et al., 2025 )
DiT-L/2
256×256
Latent
11.20
0.48
90
1.85
544M
14.2
EdifyImage ( Atzmon et al., 2024 )
DiT-L/2
256×256
Image
7.62
0.47
95
2.10
602M
28.9
Table 1: Evaluations on CelebA-HQ. For all multi-scale methods (EdifyImage ( Atzmon et al., 2024 ) , Pyramidal Flow ( Jin et al., 2025 ) , Relay Diffusion ( Teng et al., 2024 ) , and ours), we report averaged GFLOPs and time during inference.
Figure 3: Qualitative results on CelebA-HQ 1024 (left two), 512 (middle two), and 256 (right).
Table 2: Ablation studies on CelebA-HQ. We analyze various design choices, including VAE architecture, mixture-of-Transformer (MoT) design, noise schedule, and other modeling configurations. We report FID-50K scores on 256×256 resolution images. Our default settings are marked in gray .
Methods
Backbone
Training Steps
CFG
FID
NFE
Time (s)
GFLOPs
DiT ( Peebles and Xie, 2023 )
DiT-B/2
600 K
×
41.27
250
1.87
5.6
LFM ( Dao et al., 2023 )
DiT-B/2
600 K
×
48.29
89
1.70
5.6
Pyramidal Flow ( Jin et al., 2025 )
DiT-B/2
600 K
×
39.40
90
1.74
5.7
Ours
DiT-B/2
600 K
×
36.50
80
1.25
4.9
DiT ( Peebles and Xie, 2023 )
DiT-XL/2
600 K
×
19.50
250
3.50
29.1
LFM ( Dao et al., 2023 )
DiT-XL/2
600 K
×
28.37
89
3.32
29.1
Table 3: Results of class-conditional generation on ImageNet 256×256 .
Figure 4: Qualitative results on ImageNet 256×256 using our trained B/2 model with CFG= 1.5 .
Figure 5: FID-50K on ImageNet (256 × 256) across training iterations comparing LFM ( Dao et al., 2023 ) with ours using two backbones (B/2 and XL/2).
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Resolution
Latent size
# Scales
Decomposition
FID ↓
256 × 256
32 × 32
2
32 → 16
3.53
256 × 256
32 × 32
3
32 → 16 → 8
3.59
256 × 256
32 × 32
4
32 → 16 → 8 → 4
5.12
512 × 512
64 × 64
2
64 → 32
5.45
512 × 512
64 × 64
3
64 → 32 → 16
4.04
512 × 512
64 × 64
4
64 → 32 → 16 → 8
4.12
Appendix
Table 4: FID vs. number of Laplacian scales across 256–1024 resolutions on CelebA-HQ.
Resolution
T1
T2
FID ↓
1024 × 1024
0.67
0.33
5.51
1024 × 1024
0.90
0.33
6.72
1024 × 1024
0.67
0.10
8.12
Appendix
Table 5: Three-scale temporal segmentation ablation at 10242 resolution. Balanced allocation ( T1=0.67,T2=0.33 ) achieves the best FID, confirming the trend observed in the two-scale case.
Noise schedule σt(k)
Coupling schedule αt(k)
FID ↓ (256 2 )
1−t (Linear)
1−Tk+1t−Tk+1 (Linear)
3.53
cos(2πt) (GVP)
sin(2(1−Tk+1)π(t−Tk+1)) (GVP)
4.10
(1−t)2 (Quadratic)
1−Tk+1t−Tk+1 (Linear)
3.78
(1−t)3 (Cubic)
1−Tk+1t−Tk+1 (Linear)
4.25
Appendix
Table 11
Training Details
CelebA-HQ 256
CelebA-HQ 512
CelebA-HQ 1024
ImageNet 256
Backbone
DiT-L/2
DiT-L/2
DiT-L/2
DiT-B/2 / DiT-XL/2
Largest latent size
32 × 32
64 × 64
128 × 128
32 × 32
Batch size
256
256
128
256
Init LR
2e-4
2e-4
2e-4
1e-4
LR schedule
CosineAnnealingLR
CosineAnnealingLR
CosineAnnealingLR
N/A
Final LR
1e-6
1e-6
1e-6
N/A
Appendix
Table 6: Training details across datasets and resolutions. We summarize hyperparameters, computation complexity, and resource usage across benchmarks. Training time and speed may fluctuate due to hardware conditions.
Flow matching models have emerged as a powerful framework for realistic image generation by learning to reverse a corruption process that progressively adds Gaussian noise. However, because noise is injected in the latent domain, its impact on different frequency components is non-uniform. As a result, during inference, flow matching models tend to generate low-frequency components (global structure) in the early stages, while high-frequency components (fine details) emerge only later in the reverse process. Building on this insight, we propose Frequency-Aware Flow Matching (FreqFlow), a novel approach that explicitly incorporates frequency-aware conditioning into the flow matching framework via time-dependent adaptive weighting. We introduce a two-branch architecture: (1) a frequency branch that separately processes low- and high-frequency components to capture global structure and refine textures and edges, and (2) a spatial branch that synthesizes images in the latent domain, guided by the frequency branch's output. By explicitly integrating frequency information into the generation process, FreqFlow ensures that both large-scale coherence and fine-grained details are effectively modeled low-frequency conditioning reinforces global structure, while high-frequency conditioning enhances texture fidelity and detail sharpness. On the class-conditional ImageNet-256 generation benchmark, our method achieves state-of-the-art performance with an FID of 1.38, surpassing the prior diffusion model DiT and flow matching model SiT by 0.79 and 0.58 FID, respectively. Code is available at https://github.com/OliverRensu/FreqFlow.
Pixel-space generative models bypass lossy latent compression, yet necessitate joint learning of global structure and fine-grained details in a high-dimensional space. Standard flow matching interpolates noise toward a fixed clean-image endpoint, leaving the spectral evolution to be learned implicitly. In this paper, we introduce Energy-Guided Flow Matching(EG-FM) that explicitly models a coarse-to-fine generative trajectory by moving endpoint. Specifically, EG-FM replaces the fixed endpoint with a heat-kernel-filtered endpoint that evolves smoothly from low-frequency image to clean image. The fraction of high-frequency signal in moving endpoint is released by an image-specific energy-guided scheduling, leading to the re-targeting of velocity in flow matching. Our framework requires no adaptation of the backbone and training data, bringing negligible cost on the training and inference stages. In our experiment, EG-FM consistently achieves lower FID on the ImageNet class-conditional image generation task at 256×256 with fewer epochs, reaching an FID of 1.55 at 200 epochs and 1.45 at 600 epochs. We continue training the generation task on the setting of 512×512 resolution, yielding a FID of 1.58 after only 40 high-resolution adaptation epochs. Furthermore, we transfer EG-FM on text-to-image generation and achieve 0.85 on GenEval score and 83.9 on DPG-Bench. Code is available at https://github.com/ysng123/EG-FM.
Haoyang Tong, Yu He, Fang Li +6
MAIS & NLPR, CASIA · JD.com · Xi'an Jiaotong University +1
Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit unexpected scaling behavior. We argue that this dependence arises from the model's training objective, which poses a denoising task with little incentive to learn semantic representations. We introduce Self-Flow: a self-supervised flow matching paradigm that integrates representation learning within the generative framework. Our key mechanism, Dual-Timestep Scheduling, applies heterogeneous noise levels across tokens, creating an information asymmetry that forces the model to infer missing information from corrupted inputs. This drives learning strong representations alongside generative capabilities without external supervision. Our method generalizes across modalities and enables multi-modal training while following expected scaling laws, achieving superior image, video, and audio generation.