DyWeight: Dynamic Gradient Weighting for Few-Step Diffusion Sampling

Tong Zhao; Mingkun Lei; Liangyu Yuan; Yanming Yang; Chenxi Song; Yang Wang; Beier Zhu; Chi Zhang

cs.CVMar 12, 2026

DyWeight: Dynamic Gradient Weighting for Few-Step Diffusion Sampling

Authors: Tong Zhao, Mingkun Lei, Liangyu Yuan, Yanming Yang, Chenxi Song, Yang Wang, Beier Zhu, Chi Zhang

Organizations: Zhejiang University · AGI Lab, Westlake University · TongJi University · University of Science and Technology of China

Abstract

Diffusion Models (DMs) have achieved state-of-the-art generative performance across multiple modalities, yet their sampling process remains prohibitively slow due to the need for hundreds of function evaluations. Recent progress in multi-step ODE solvers has greatly improved efficiency by reusing historical gradients, but existing methods rely on handcrafted coefficients that fail to adapt to the non-stationary dynamics of diffusion sampling. To address this limitation, we propose Dynamic Gradient Weighting (DyWeight), a lightweight, learning-based multi-step solver that introduces a streamlined implicit coupling paradigm. By relaxing classical numerical constraints, DyWeight learns unconstrained time-varying parameters that adaptively aggregate historical gradients while intrinsically scaling the effective step size. This implicit time calibration accurately aligns the solver's numerical trajectory with the model's internal denoising dynamics under large integration steps, avoiding complex decoupled parameterizations and optimizations. Extensive experiments on CIFAR-10, FFHQ, AFHQv2, ImageNet64, LSUN-Bedroom, Stable Diffusion and FLUX.1-dev demonstrate that DyWeight achieves superior visual fidelity and stability with significantly fewer function evaluations, establishing a new state-of-the-art among efficient diffusion solvers. Code is available at https://github.com/Westlake-AGI-Lab/DyWeight

Figures & tables

Figure 2: Overview of DyWeight . Our method dynamically aggregates buffered historical gradients ( $w_{t_{n},j}\cdot\mathbf{v}_{\text{buffer}}$ ) using unconstrained learned weights ( i.e . , not requiring $\sum w=1$ ). The unnormalized sum part adjusts the effective step size via time calibration ( $t_{n}\rightarrow{\color[rgb]{0.9727,0.4805,0.4648}\tilde{t}_{n}}$ ). As illustrated on the right, DyWeight exhibits a distinct advantage in few-step generation scenarios.

Panel of Figure 3 — Figure 3: L2 error under different complexity and steps settings. (a) Error vs. Complexity: We fix the solver steps ( $S$ ) and increase the problem complexity (polynomial order $K$ ). (b) Error vs. Steps: We fix the complexity and decrease the number of solver steps.

Panel of Figure 4 — Figure 4: Effect of Time Shifting on Training Stability. We compare the (a) standard deviation of a gradient term specific to an intermediate point (expected $=\!1$ ) and (b) training loss for a 5-NFE student solver on CIFAR-10 [ 21 ] . The solver w/o time shifting ( red ) exhibits extreme variance and an unstable loss. In contrast, our proposed time shifting ( blue ) stabilizes the gradient variance around the expected value of 1.0 and achieves a smoother, lower-variance, and faster-converging training loss.

Table 1: Image generation FID

\downarrow

[ 11 ] results across six datasets, pixel space : (a) CIFAR-10 (

32\times 32

) [ 21 ] , (b) FFHQ (

64\times 64

) [ 16 ] , (c) AFHQv2 (

64\times 64

) [ 4 ] , (d) ImageNet (

64\times 64

) [ 39 ] , and latent space : (e) LSUN-Bedroom (

256\times 256

) [ 59 ] , (f) MS-COCO (

512\times 512

) [ 26 ] with Stable-Diffusion-v1.5 (SD-v1.5) [ 37 ] . We compared our DyWeight with (1) Training-free multi-step solvers: iPNDM [ 60 , 28 ] , DPM-Solver++ [ 30 ] , and UniPC [ 61 ] , (2) Learnable single-step and multi-step solvers: AMED-Solver and AMED-Plugin [ 63 ] , EPD-Solver and EPD-Plugin [ 64 ] , LD3 [ 50 ] (we report the best FID results achieved by LD3 across different multi-step solvers) and DLMS [ 25 ] . The best results are in bold , the second best are underlined . See Appendix E.1 for complete results.

Metrics	Method	NFE=3	NFE=5	NFE=7
FID $\downarrow$	DPM-Solver++(2M) [ 30 ]	63.64	21.81	22.18
	iPNDM(2M) [ 28 , 60 ]	48.46	25.03	22.22
	DyWeight (ours)	42.69	21.02	20.69
CLIP $\uparrow$	DPM-Solver++(2M) [ 30 ]	24.40	26.38	26.20
	iPNDM(2M) [ 28 , 60 ]	24.83	26.37	26.17
	DyWeight (ours)	25.43	26.73	26.49

Table 2: Performance comparison on FLUX.1-dev [ 23 ] for text-to-image generation, evaluated on MS-COCO (512

\times

512) [ 26 ] . DyWeight consistently outperforms competitive solvers in both FID [ 11 ] and CLIP score [ 35 ] .

Metrics	Method	NFE=5	NFE=7	NFE=9
CLIP $\uparrow$	DPM-Solver++(2M) [ 30 ]	26.95	27.35	27.36
	iPNDM(2M) [ 28 , 60 ]	26.95	27.10	27.14
	DyWeight (ours)	27.48	27.75	27.63
HPSv2.1 $\uparrow$	DPM-Solver++(2M) [ 30 ]	0.271	0.286	0.291
	iPNDM(2M) [ 28 , 60 ]	0.273	0.286	0.291
	DyWeight (ours)	0.279	0.288	0.293

Table 3: Performance comparison on FLUX.1-dev [ 23 ] for text-to-image generation, evaluated on Drawbench [ 42 ] . DyWeight consistently outperforms competitive solvers in CLIP score [ 35 ] , HPSv2.1 [ 55 ] and ImageReward [ 57 ] .

Method	NFE (1 Step = 2 NFEs with CFG [ 13 ] )
Method	8	12	16	20
iPNDM(2M) [ 60 , 28 ]	28.33	29.79	30.15	30.30
DPM-Solver++(2M) [ 30 ]	28.50	28.65	29.65	30.02
UniPC(2M) [ 61 ]	26.44	29.05	29.79	30.08
DyWeight (ours)	28.56	29.81	30.17	30.05

Table 4: CLIP-Score

\uparrow

[ 35 ] results on Stable-Diffusion-v1.5 [ 37 ] .

Figure 5: Training convergence on CIFAR-10 (200K training images). We track training loss (left) and generation FID (right) against optimization progress under various solver configurations. As shown, our framework exhibits extreme sample efficiency, achieving massive performance gains with merely

\sim\mathbf{600}

images.

Panel of Figure 6 — Figure 6: Ablation studies. (a, b) Impact of time calibration components on CIFAR-10 [ 21 ] and FFHQ [ 16 ] . Both time shifting and time scaling are essential for optimal performance. (c) Sensitivity to multi-step order $K$ on CIFAR-10 [ 21 ] , showing $K=3$ is optimal.

Teacher Solver ( $M$ steps)	NFE
Teacher Solver ( $M$ steps)	3	5	7	9
iPNDM (18) [ 60 , 28 ]	9.06	3.33	2.47	2.28
iPNDM (35) [ 60 , 28 ]	8.16	3.02	2.40	2.13
iPNDM (50) [ 60 , 28 ]	8.70	3.23	2.39	2.29
DPM-Solver-2 (35) [ 31 ]	8.77	3.17	2.44	2.24
Heun (35) [ 15 ]	8.80	3.09	2.28	2.12

Table 5: Robustness to teacher solver on CIFAR-10 [ 21 ] . Numbers in parentheses denote teacher steps. Student performance is stable across different high-fidelity teacher solvers and step counts.

Appendix figures & tables34 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1 : Visualization of the learned coefficients across different datasets at 3 and 4 NFEs. Each row represents the learned parameters for a specific denoising step, starting with the Analytical First Step (AFS) [ 5 ] in the first row. The columns explicitly detail the unconstrained historical gradient weights (

w_{n,i}

), followed by their unnormalized sum (

\sum w_{n,i}

) and the time scaling factor (

s_{n}

Dataset / Coeff.	C.-CIFAR	C.-ImgNet	C.-FFHQ	C.-LSUN	iPNDM
CIFAR-10 [ 21 ]	8.16	14.04	16.41	14.86	24.55
ImageNet [ 39 ]	25.18	17.37	21.20	20.11	34.81
FFHQ [ 16 ]	33.89	16.64	16.78	21.49	27.72
LSUN-Bed [ 59 ]	56.52	27.58	54.53	12.65	34.81

Appendix

Table A.1 : Cross-dataset evaluation of learned coefficients. We evaluate the transferability of 3-NFE parameters trained on one dataset (columns, denoted by “C.-”) across different evaluation distributions (rows). Native coefficients generally provide the most stable performance (diagonal).

CIFAR-10 [ 21 ]
Supervision strategy	NFE
Supervision strategy	3	5	7	9
iPNDM [ 28 , 60 ]	24.55	7.77	4.04	2.83
DyWeight - path	11.74	4.44	2.91	2.38
DyWeight - endpoint	8.16	3.02	2.40	2.13
ImageNet-64 [ 39 ]

Appendix

Table A.2 : Comparison of supervision strategies for training. We compare trajectory-based ( path ) supervision against terminal-state ( endpoint ) supervision . Path supervision computes the loss at every intermediate steps, forcing the student to strictly mimic the teacher’s trajectory. In contrast, endpoint supervision only supervises the final output, consistently yielding better results.

Weights initialization
Dataset / NFE	CIFAR-10 [ 21 ]			AFHQv2 [ 4 ]
Dataset / NFE	4	6	8	4	6	8
Adams-Bashforth [ 9 , 1 ]	3.92	2.61	2.18	5.38	2.66	2.23
Euler [ 9 , 1 ]	6.46	3.92	2.80	8.26	4.19	2.77
Uniform	9.40	5.40	4.39	10.25	7.86	5.76
Time schedule initialization

Appendix

Table A.3 : Comparison of different initialization strategies for DyWeight . We report the FID [ 11 ] scores of different initialization methods across varying NFEs and datasets, all optimized using 10K training pairs. Top: Comparison of gradient weights initialization strategies. Adams-Bashforth [ 9 , 1 ] initializes weights using standard coefficients (iPNDM [ 28 , 60 ] ); Euler [ 9 , 1 ] sets the current step weight to 1 and others to 0; Uniform distributes weights evenly. Bottom: Comparison of time schedule initialization methods. We set

\rho=7

for the EDM (Polynomial) [ 15 ] schedule and

\rho=1

for the Time Uniform schedule.

Size	CIFAR-10 [ 21 ]			ImageNet [ 39 ]
Size	NFE=4	NFE=6	NFE=8	NFE=4	NFE=6	NFE=8
10K	3.92	2.63	2.26	11.48	6.15	4.69
20K	4.09	2.61	2.18	12.94	5.80	5.02
30K	4.35	2.68	2.41	13.32	6.16	4.68

Appendix

Table A.4 : Impact of distillation dataset size (number of teacher samples) on CIFAR-10 [ 21 ] and ImageNet [ 39 ] . Performance saturates at 10K samples, demonstrating data efficiency.

Panel of Figure 16 — Figure A.2 : Complete results of the numerical study. L2 error under different complexity and steps settings. (a) – (h) Error vs. Complexity: We fix the solver steps ( $S$ ) and increase the problem complexity (polynomial order $K$ ). (i) – (p) Error vs. Steps: We fix the complexity ( $K$ ) and decrease the number of solver steps ( $S$ ).

Method	NFE
Method	3	4	5	6	7	8	9
iPNDM [ 60 , 28 ]	24.55	13.92	7.77	5.07	4.04	3.22	2.83
DPM-Solver++(3M) [ 30 ]	55.76	22.41	9.94	5.97	4.29	3.37	2.99
UniPC [ 61 ]	109.60	45.20	23.98	11.14	5.83	3.99	3.21
AMED-Solver [ 63 ]	18.49	17.18	7.59	7.04	4.36	5.56	3.67
AMED-Plugin [ 63 ]	10.81	-	6.61	-	3.65	-	2.63

Appendix

Table A.5 : Image generation FID

\downarrow

[ 11 ] on CIFAR-10(

32\times 32

) [ 21 ] . The best results are in bold , the second best are underlined .

Method	NFE
Method	3	4	5	6	7	8	9
iPNDM [ 60 , 28 ]	27.72	20.07	13.80	8.61	7.16	5.43	4.98
DPM-Solver++(3M) [ 30 ]	66.07	30.06	13.47	8.25	6.20	5.20	4.77
UniPC [ 61 ]	86.43	44.78	21.40	12.85	7.44	5.50	4.47
AMED-Solver [ 63 ]	47.31	26.89	14.80	9.97	8,82	7.86	6.31
AMED-Plugin [ 63 ]	26.87	-	12.49	-	6.64	-	4.24

Appendix

Table A.6 : Image generation FID

\downarrow

[ 11 ] on FFHQ(

64\times 64

) [ 16 ] . The best results are in bold , the second best are underlined .

Method	NFE
Method	3	4	5	6	7	8	9
iPNDM [ 60 , 28 ]	15.53	8.73	5.58	3.81	3.19	2.72	2.48
DPM-Solver++(3M) [ 30 ]	35.05	21.04	10.63	6.24	4.47	3.86	3.44
UniPC [ 61 ]	60.89	33.78	13.01	8.27	5.07	4.60	4.46
AMED-Solver [ 63 ]	31.82	18.99	7.34	8.19	4.39	5.55	3.53
LD3 [ 50 ]	17.94	9.96	6.09	3.63	2.97	2.63	2.27

Appendix

Table A.7 : Image generation FID

\downarrow

[ 11 ] on AFHQv2(

64\times 64

) [ 4 ] . The best results are in bold , the second best are underlined .

Method	NFE
Method	3	4	5	6	7	8	9
iPNDM [ 60 , 28 ]	34.81	21.33	15.54	10.27	8.64	6.60	5.64
DPM-Solver++(3M) [ 30 ]	65.19	30.56	16.87	11.38	8.68	7.12	6.25
UniPC [ 61 ]	91.38	55.63	24.36	14.30	9.57	7.52	6.34
AMED-Solver [ 63 ]	38.10	32.69	10.74	10.63	6.66	7.71	5.44
AMED-Plugin [ 63 ]	28.06	-	13.83	-	7.81	-	5.60

Appendix

Table A.8 : Image generation FID

\downarrow

[ 11 ] on ImageNet(

64\times 64

) [ 39 ] . The best results are in bold , the second best are underlined .

Method	NFE
Method	3	4	5	6	7	8	9
iPNDM [ 60 , 28 ]	43.31	26.14	18.46	12.81	11.03	9.49	7.89
DPM-Solver++(3M) [ 30 ]	111.90	48.49	18.44	8.39	5.18	4.12	3.77
UniPC [ 61 ]	112.30	39.66	13.76	6.46	4.52	3.96	3.72
AMED-Solver [ 63 ]	58.21	15.67	13.20	8.92	7.10	4.19	5.65
AMED-Plugin [ 63 ]	101.5	-	25.68	-	8.63	-	7.82

Appendix

Table A.9 : Image generation FID

\downarrow

[ 11 ] on LSUN-Bedroom(

256\times 256

) [ 59 ] . The best results are in bold , the second best are underlined .

Panel of Figure 22 — Figure A.3 : Qualitative comparison on CIFAR-10 ( $32\times 32$ ) [ 21 ] at 3 NFEs. DyWeight exhibits significantly reduced noise and better structure compared to iPNDM [ 28 , 60 ] .

Panel of Figure 23 — Figure A.4 : Qualitative comparison on CIFAR-10 ( $32\times 32$ ) [ 21 ] at 4 NFEs. DyWeight exhibits significantly reduced noise and better structure compared to iPNDM [ 28 , 60 ] .

Panel of Figure 24 — Figure A.5 : Qualitative comparison on CIFAR-10 ( $32\times 32$ ) [ 21 ] at 5 NFEs. DyWeight exhibits significantly reduced noise and better structure compared to iPNDM [ 28 , 60 ] .

Panel of Figure 25 — Figure A.6 : Qualitative comparison on FFHQ ( $64\times 64$ ) [ 16 ] at 3 NFEs. DyWeight yields fewer artifacts and clearer facial details compared with iPNDM [ 28 , 60 ] .

Panel of Figure 26 — Figure A.7 : Qualitative comparison on FFHQ ( $64\times 64$ ) [ 16 ] at 4 NFEs. DyWeight yields fewer artifacts and clearer facial details compared with iPNDM [ 28 , 60 ] .

Panel of Figure 27 — Figure A.8 : Qualitative comparison on FFHQ ( $64\times 64$ ) [ 16 ] at 5 NFEs. DyWeight yields fewer artifacts and clearer facial details compared with iPNDM [ 28 , 60 ] .

Panel of Figure 28 — Figure A.9 : Qualitative comparison on AFHQv2 ( $64\times 64$ ) [ 4 ] at 3 NFEs. DyWeight produces animal features with higher fidelity and noticeably less blurring compared with iPNDM [ 28 , 60 ] .

Panel of Figure 29 — Figure A.10 : Qualitative comparison on AFHQv2 ( $64\times 64$ ) [ 4 ] at 4 NFEs. DyWeight produces animal features with higher fidelity and noticeably less blurring compared with iPNDM [ 28 , 60 ] .

Panel of Figure 30 — Figure A.11 : Qualitative comparison on AFHQv2 ( $64\times 64$ ) [ 4 ] at 5 NFEs. DyWeight produces animal features with higher fidelity and noticeably less blurring compared with iPNDM [ 28 , 60 ] .

Panel of Figure 31 — Figure A.12 : Qualitative comparison on ImageNet ( $64\times 64$ ) [ 39 ] at 3 NFEs. DyWeight generates recognizable object classes with reduced noise compared to iPNDM [ 28 , 60 ] .

Panel of Figure 32 — Figure A.13 : Qualitative comparison on ImageNet ( $64\times 64$ ) [ 39 ] at 4 NFEs. DyWeight generates recognizable object classes with reduced noise compared to iPNDM [ 28 , 60 ] .

Panel of Figure 33 — Figure A.14 : Qualitative comparison on ImageNet ( $64\times 64$ ) [ 39 ] at 5 NFEs. DyWeight generates recognizable object classes with reduced noise compared to iPNDM [ 28 , 60 ] .

Panel of Figure 34 — Figure A.15 : Qualitative comparison on LSUN-Bedroom ( $256\times 256$ ) [ 59 ] at 3 NFEs. DyWeight preserves global room layout and structure, reduces blur, and enhances object details compared with iPNDM [ 28 , 60 ] .

Panel of Figure 35 — Figure A.16 : Qualitative comparison on LSUN-Bedroom ( $256\times 256$ ) [ 59 ] at 4 NFEs. DyWeight preserves global room layout and structure, reduces blur, and enhances object details compared with iPNDM [ 28 , 60 ] .

Panel of Figure 36 — Figure A.17 : Qualitative comparison on LSUN-Bedroom ( $256\times 256$ ) [ 59 ] at 5 NFEs. DyWeight preserves global room layout and structure, reduces blur, and enhances object details compared with iPNDM [ 28 , 60 ] .

Panel of Figure 37 — Figure A.18 : Qualitative comparison on SD v1.5 [ 37 ] (MS-COCO [ 26 ] ) at 8 NFEs (4 Steps). Our method generates more detailed textures and coherent objects with reduced noise compared to iPNDM [ 28 , 60 ] . Prompts : (1) A small bird standing on top of a sidewalk. (2) a close up of a cat on the ground near a chair. (3) Teddy bear in front of a holly covered object. (4) An empty boat in the water near a tree.

Panel of Figure 38 — Figure A.19 : Qualitative comparison on SD v1.5 [ 37 ] (MS-COCO [ 26 ] ) at 12 NFEs (6 Steps). Our method generates more detailed textures and coherent objects with reduced noise compared to iPNDM [ 28 , 60 ] . Prompts : (1) A small bird standing on top of a sidewalk. (2) a close up of a cat on the ground near a chair. (3) Teddy bear in front of a holly covered object. (4) An empty boat in the water near a tree.

Panel of Figure 39 — Figure A.20 : Qualitative comparison on SD v1.5 [ 37 ] (MS-COCO [ 26 ] ) at 16 NFEs (8 Steps). Our method generates more detailed textures and coherent objects with reduced noise compared to iPNDM [ 28 , 60 ] . Prompts : (1) A small bird standing on top of a sidewalk. (2) a close up of a cat on the ground near a chair. (3) Teddy bear in front of a holly covered object. (4) An empty boat in the water near a tree.

Figure A.21 : Qualitative comparison on FLUX.1-dev [ 23 , 22 ] at 5 NFEs. From top to bottom, the rows show results from DPM-Solver++(2M) [ 30 ] , iPNDM(2M) [ 28 , 60 ] , and our DyWeight . Our method delivers superior visual fidelity, prompt alignment, and structural coherence.

Figure A.22 : Qualitative comparison on FLUX.1-dev [ 23 , 22 ] at 5 NFEs. From top to bottom, the rows show results from DPM-Solver++(2M) [ 30 ] , iPNDM(2M) [ 28 , 60 ] , and our DyWeight . Our method delivers superior visual fidelity, prompt alignment, and structural coherence.

Figure A.23 : Qualitative comparison on FLUX.1-dev [ 23 , 22 ] at 7 NFEs. From top to bottom, the rows show results from DPM-Solver++(2M) [ 30 ] , iPNDM(2M) [ 28 , 60 ] , and our DyWeight . Our method delivers superior visual fidelity, prompt alignment, and structural coherence.

Figure A.24 : Qualitative comparison on FLUX.1-dev [ 23 , 22 ] at 7 NFEs. From top to bottom, the rows show results from DPM-Solver++(2M) [ 30 ] , iPNDM(2M) [ 28 , 60 ] , and our DyWeight . Our method delivers superior visual fidelity, prompt alignment, and structural coherence.

Figure A.25 : Comprehensive list of text prompts employed for the FLUX.1-dev [ 23 , 22 ] qualitative comparisons.

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Dual-Solver: A Generalized ODE Solver for Diffusion Models with Dual Prediction

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SteAI · MODULABS · Korea University

Diffusion Model Inference Acceleration Few-Step Diffusion Sampling

Open paper AskPDF arXiv

Diffusion models achieve state-of-the-art image quality. However, sampling is costly at inference time because it requires a large number of function evaluations (NFEs). To reduce NFEs, classical ODE numerical methods have been adopted. Yet, the choice of prediction type and integration domain leads to different sampling behaviors. To address these issues, we introduce Dual-Solver, which generalizes multistep samplers through learnable parameters that continuously (i) interpolate among prediction types, (ii) select the integration domain, and (iii) adjust the residual terms. It retains the standard predictor-corrector structure while preserving second-order local accuracy. These parameters are learned via a classification-based objective using a frozen pretrained classifier (e.g., MobileNet or CLIP). For ImageNet class-conditional generation (DiT, GM-DiT) and text-to-image generation (SANA, PixArt-

α

), Dual-Solver improves FID and CLIP scores in the low-NFE regime (

3 \le

NFE

\le 9

) across backbones.

Abstract

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