Official project page and code release

Energy-Guided Flow Matching

Haoyang Tong^*1,2, Yu He^*2, Fang Li², Lichen Ma^2,3, Jingling Fu², Dong Chen², Zhen Chen², Junshi Huang², Jie Cao^✉1

¹ MAIS & NLPR, CASIA ² JD.com ³ Xi’an Jiaotong University

tonghaoyang22@mails.ucas.ac.cn, heyu2579@gmail.com, jie.cao@cripac.ia.ac.cn

^*Equal contribution Corresponding author

EG-FM explicitly models a coarse-to-fine generative trajectory by progressively releasing image frequency information through a sample-adaptive moving endpoint.

Paper Code ImageNet Checkpoint T2I Checkpoint Coming Soon Results

EG-FM reaches 1.55 FID at 200 epochs—approximately 4× faster than PixelDiT-XL.

ImageNet-256 · FID vs. training epochs

Faster convergence with EG-FM

Hover or focus a point for its value. Select a legend item to compare individual series.

Abstract

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.

Method

Energy-Guided Flow Matching constructs an image-adaptive coarse-to-fine trajectory by replacing the fixed clean-image endpoint with a moving, heat-kernel-filtered endpoint. Each image follows its own spectral energy schedule, progressively revealing structure and detail while retaining an exact analytical velocity target for standard flow-matching training.

Overview of Energy-Guided Flow Matching from Figure 2 of the paper

Experiments

Quantitative results

Controlled comparisons across class-conditional and text-to-image generation.

ImageNet metrics use 50K generated samples and the ADM evaluation suite. Best EG-FM results are highlighted.

ImageNet 256 × 256

Class-conditional generation

Table 1

Method	Epochs	Params	NFE	FID ↓	sFID ↓	IS ↑	Prec. ↑	Recall ↑
REPA	800	675M	250×2	1.42	4.70	305.7	0.80	0.65
DDT-XL	400	675M	—	1.26	—	310.6	0.79	0.65
RAE-XL	800	839M	—	1.13	—	262.6	0.78	0.67
PixelFlow-XL	320	677M	120×2	1.98	5.83	282.1	0.81	0.60
PixNerd-XL	320	700M	100×2	1.93	—	298.0	0.80	0.60
JiT-G	600	2.0B	100×2	1.82	—	292.6	0.79	0.62
PixelU-H/16	600	1.17B	100×2	1.63	5.04	305.9	0.79	0.64
DiP-XL/16	600	631M	100×2	1.79	4.59	281.9	0.80	0.63
FREPix-XL	320	674M	100×2	1.91	4.59	295.6	0.79	0.62
DeCo-XL/16	600	682M	100×2	1.69	4.59	304.0	0.79	0.63
+ EG-FM	440	682M	100×2	1.63	4.78	300.1	0.79	0.62
HyperDiT-H	600	952M	100×2	1.56	4.73	306.5	0.80	0.64
+ EG-FM	220	952M	100×2	1.51	4.31	293.4	0.78	0.64
PixelDiT-XL	80	797M	100×2	2.36	5.11	282.3	0.80	0.57
PixelDiT-XL	320	797M	100×2	1.61	4.68	292.7	0.78	0.64
PixelDiT-XL	800	797M	100×2	1.54	4.49	297.0	0.78	0.65
+ EG-FM	80	797M	100×2	1.99	5.09	280.8	0.81	0.61
+ EG-FM	200	797M	100×2	1.55	4.60	296.2	0.79	0.65
+ EG-FM	600	797M	100×2	1.45	4.41	299.6	0.78	0.65

ImageNet 512 × 512

High-resolution class-conditional generation

Table 7

Method	Epochs	Params	NFE	FID ↓	sFID ↓	IS ↑	Prec. ↑	Recall ↑
DiT-XL/2	600	675M	250×2	3.04	5.02	240.8	0.84	0.54
SiT-XL/2	600	675M	250×2	2.62	4.18	252.2	0.84	0.57
REPA	200	675M	250×2	2.08	4.19	274.6	0.83	0.58
PixNerd-XL†	320	700M	100×2	2.84	5.95	245.6	0.80	0.59
JiT-H	600	956M	100×2	1.94	—	309.1	—	—
PixelU-H/32	600	1.2B	100×2	1.92	5.98	322.1	0.80	0.58
DiP-XL/32	—	631M	100×2	2.31	4.48	291.7	0.84	0.58
DeCo-XL/16†	340	682M	100×2	2.22	4.67	290.0	0.80	0.60
PixelDiT-XL†	850	797M	100×2	1.81	5.61	278.6	0.78	0.67
+ EG-FM†	240	797M	100×2	1.68	4.77	295.5	0.79	0.63
HyperDiT-H + EG-FM†	260	952M	100×2	1.58	4.90	285.0	0.79	0.64

† Continued training from a 256 × 256 checkpoint. NFE includes conditional and unconditional classifier-free-guidance evaluations.

GenEval at 512 × 512

Category-wise text-to-image evaluation

Appendix Table 8

Method	Params	Single obj. ↑	Two obj. ↑	Counting ↑	Colors ↑	Position ↑	Color attr. ↑	Overall ↑
PixArt-α	0.6B	0.98	0.50	0.44	0.80	0.08	0.07	0.48
SD3	8B	0.98	0.84	0.66	0.74	0.40	0.43	0.68
FLUX.1-dev	12B	0.99	0.81	0.79	0.74	0.20	0.47	0.67
DALL-E 3	—	0.96	0.87	0.47	0.83	0.43	0.45	0.67
BLIP3o	4B	—	—	—	—	—	—	0.81
OmniGen2	4B	1.00	0.95	0.64	0.88	0.55	0.76	0.80
PixelFlow	0.9B	—	—	—	—	—	—	0.60
PixNerd	1.2B	0.97	0.86	0.44	0.83	0.71	0.53	0.73
DeCo-XXL/16	1.1B	1.00	0.92	0.72	0.91	0.80	0.79	0.86
PixelDiT-T2I	1.3B	1.00	0.94	0.70	0.90	0.53	0.65	0.78
EG-FM-T2I	1.3B	1.00	0.95	0.74	0.92	0.72	0.77	0.85

DPG-Bench at 512 × 512

Category-wise dense-prompt evaluation

Appendix Table 9

Method	Params	Global ↑	Entity ↑	Attribute ↑	Relation ↑	Other ↑	Overall ↑
PixArt-α	0.6B	81.7	80.1	80.4	81.7	76.5	71.6
PixArt-Σ	0.6B	87.5	87.1	86.5	84.0	86.1	79.5
PixelFlow	0.9B	—	—	—	—	—	77.9
PixNerd	1.2B	80.5	87.9	87.2	91.3	72.8	80.9
DeCo-XXL/16	1.1B	—	—	—	—	—	81.4
PixelDiT-T2I	1.3B	88.0	90.9	87.6	89.8	88.5	83.7
EG-FM-T2I	1.3B	89.3	89.2	90.2	90.9	89.7	83.9

Appendix Tables 8 and 9 decompose aggregate text alignment into object, counting, color, spatial, entity, attribute, and relation capabilities. A dash indicates an unreported item.

Qualitative results

The main qualitative overview from the paper.

Qualitative class-conditional and text-to-image samples generated with EG-FM

Text-to-image samples generated with EG-FM.

Citation

If you find this work useful, please cite:

@article{tong2026energy,
  title   = {Energy-Guided Flow Matching},
  author  = {Tong, Haoyang and He, Yu and Li, Fang and Ma, Lichen and Fu, Jingling and Chen, Dong and Chen, Zhen and Huang, Junshi and Cao, Jie},
  journal = {arXiv preprint arXiv:2608.05811},
  year    = {2026}
}