Laplacian Multi-scale Flow Matching for Generative Modeling

Zelin Zhao; Petr Molodyk; Haotian Xue; Yongxin Chen

cs.CVFeb 23, 2026

Laplacian Multi-scale Flow Matching for Generative Modeling

Authors: Zelin Zhao, Petr Molodyk, Haotian Xue, Yongxin Chen

Organizations: Georgia Institute of Technology Atlanta, GA 30332, USA

Abstract

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 $\times$ 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 $T_{2}$ , $T_{1}$ 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 $t=T_{2}$ , then progressively conditions finer scales on completed coarser scales ( $t=T_{2}$ to $T_{1}$ and $t=T_{1}$ 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

V_{\theta}

. 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 $\downarrow$	Recall $\uparrow$	NFE	Time (s)	Params	GFLOPs
Standard Resolution (256)
FM ( Lipman et al., 2023 )	U-Net	$256\times 256$	Image	7.34	-	128	-	-	-
LDM ( Rombach et al., 2022 )	U-Net	$256\times 256$	Latent	5.11	0.49	50	2.90	150M	10.2
LFM ( Dao et al., 2023 )	DiT-L/2	$256\times 256$	Latent	5.26	0.46	89	1.70	541M	22.1
Pyramidal Flow ( Jin et al., 2025 )	DiT-L/2	$256\times 256$	Latent	11.20	0.48	90	1.85	544M	14.2
EdifyImage ( Atzmon et al., 2024 )	DiT-L/2	$256\times 256$	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\times 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	$\times$	41.27	250	1.87	5.6
LFM ( Dao et al., 2023 )	DiT-B/2	$600$ K	$\times$	48.29	89	1.70	5.6
Pyramidal Flow ( Jin et al., 2025 )	DiT-B/2	$600$ K	$\times$	39.40	90	1.74	5.7
Ours	DiT-B/2	$600$ K	$\times$	36.50	80	1.25	4.9
DiT ( Peebles and Xie, 2023 )	DiT-XL/2	$600$ K	$\times$	19.50	250	3.50	29.1
LFM ( Dao et al., 2023 )	DiT-XL/2	$600$ K	$\times$	28.37	89	3.32	29.1

Table 3: Results of class-conditional generation on ImageNet

256\times 256

Figure 4: Qualitative results on ImageNet $256\times 256$ using our trained B/2 model with CFG= $1.5$ .

Figure 5: FID-50K on ImageNet (256

\times

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 $\downarrow$
256 $\times$ 256	32 $\times$ 32	2	32 $\rightarrow$ 16	3.53
256 $\times$ 256	32 $\times$ 32	3	32 $\rightarrow$ 16 $\rightarrow$ 8	3.59
256 $\times$ 256	32 $\times$ 32	4	32 $\rightarrow$ 16 $\rightarrow$ 8 $\rightarrow$ 4	5.12
512 $\times$ 512	64 $\times$ 64	2	64 $\rightarrow$ 32	5.45
512 $\times$ 512	64 $\times$ 64	3	64 $\rightarrow$ 32 $\rightarrow$ 16	4.04
512 $\times$ 512	64 $\times$ 64	4	64 $\rightarrow$ 32 $\rightarrow$ 16 $\rightarrow$ 8	4.12

Appendix

Table 4: FID vs. number of Laplacian scales across 256–1024 resolutions on CelebA-HQ.

Resolution	$T_{1}$	$T_{2}$	FID $\downarrow$
1024 $\times$ 1024	0.67	0.33	5.51
1024 $\times$ 1024	0.90	0.33	6.72
1024 $\times$ 1024	0.67	0.10	8.12

Appendix

Table 5: Three-scale temporal segmentation ablation at

1024^{2}

resolution. Balanced allocation (

T_{1}=0.67,T_{2}=0.33

) achieves the best FID, confirming the trend observed in the two-scale case.

Noise schedule $\sigma_{t}^{(k)}$	Coupling schedule $\alpha_{t}^{(k)}$	FID $\downarrow$ (256 2 )
$1-t$ (Linear)	$\frac{t-T_{k+1}}{1-T_{k+1}}$ (Linear)	3.53
$\cos\!\left(\tfrac{\pi}{2}t\right)$ (GVP)	$\sin\!\left(\tfrac{\pi(t-T_{k+1})}{2(1-T_{k+1})}\right)$ (GVP)	4.10
$(1-t)^{2}$ (Quadratic)	$\frac{t-T_{k+1}}{1-T_{k+1}}$ (Linear)	3.78
$(1-t)^{3}$ (Cubic)	$\frac{t-T_{k+1}}{1-T_{k+1}}$ (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 $\times$ 32	64 $\times$ 64	128 $\times$ 128	32 $\times$ 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.

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Open paper AskPDF arXiv

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.

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