Learned End-to-End Guidance Schedules for Diffusion Models

Aneesh Barthakur; Mathias Niepert; Luiz F. O. Chamon

cs.LGOct 1, 2026

Learned End-to-End Guidance Schedules for Diffusion Models

Authors: Aneesh Barthakur, Mathias Niepert, Luiz F. O. Chamon

Organizations: University of Stuttgart · École polytechnique, Institut Polytechnique de Paris

Abstract

Diffusion models are a powerful generative paradigm used across multimedia and scientific applications. Guided diffusion methods impose requirements on the generation by adding the gradient of a differentiable loss (the guidance function) as a drift term during inference. The weight of this drift (the guidance scale) is critical for the trade-off between data quality and requirement satisfaction. To achieve both of these goals, guided diffusion must resort to small guidance scales and lengthy sampling, incurring high computational costs. This work proposes learned end-to-end guidance schedules (LEEGS) to achieve these objectives with fewer sampling steps. LEEGS trains a time-dependent schedule by minimizing the guidance function over a small set of examples using stochastic gradient descent. Backpropagating through guided sampling is computationally expensive, so LEEGS uses an approximation of the gradient that cuts training time by a factor of 4. We evaluate LEEGS on diverse guidance tasks, including (a) image inpainting, (b) noisy image inverse problems, (c) face-ID-guided generation, and (d) forward and inverse PDE problems, outperforming baselines at equal budget (50 or 100 NFEs), or matching constant guidance with only 10% of the steps.

Figures & tables

Dataset	Method	NFEs	Wide	Narrow	S. res. (2x)	Alternate Lines	Half
Imagenet	RePaint	200	0.186	0.18	0.622	0.394	0.368
	LEEGS (ours)	200	0.182	0.151	0.147	0.111	0.346
	RePaint	$\approx$ 2400	0.134	0.064	0.183	0.089	0.304
CelebA-HQ	RePaint	200	0.128	0.128	0.205	0.049	0.283
	LEEGS (ours)	200	0.102	0.080	0.065	0.042	0.229
	RePaint	$\approx$ 2400	0.059	0.028	0.029	0.009	0.165

Table 3: Comparison for image inpainting tasks for CelebA-HQ and Imagenet. Green (bold): best (non-reference rows).

Method	NFEs	Poisson		Helmholtz		Darcy
Method	NFEs	Forward	Inverse	Forward	Inverse	Forward	Inverse
Const.	50x2	19.34%	33.11%	27.56%	32.15%	21.54%	15.58%
Linear increase	50x1	27.59%	46.43%	39.72%	45.42%	24.70%	20.98%
Linear decrease	50x1	10.25%	29.81%	17.07%	29.84%	11.03%	14.05%
LEEGS (ours)	50x1	5.80%	29.36%	10.03%	29.71%	11.33%	17.84%
Const.	100x2	15.62%	30.10%	22.96%	29.54%	18.17%	16.71%

Table 5: Comparison for forward and inverse PDE problems with sparse observations. Green (bold): best; blue : second best (non-reference rows).

Appendix figures & tables72 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Ground truth and the 5 noisy measurement operators used for Tables 1 and 2 (FFHQ example).

FFHQ
Subtask	Avg. NFEs ( $T=25$ )	Avg. NFEs ( $T=50$ )
Box inpainting	55.7	102.8
Random inpainting	50.7	93.7
Super-resolution ( $4\times$ )	54.5	104.7
Gaussian deblur	56.0	104.4
Motion deblur	65.8	114.2

Appendix

Table 6: Average number of NFEs used by CDIM per subtask at its two settings,

T=25

and

T=50

(nominally

50

and

100

NFEs), computed over the full test set of Tables 1 and 2 .

FFHQ
Subtask	Learning rate $\eta$	Epochs	Weight decay
Super-resolution ( $4\times$ )	0.3	25 ( $S=50$ ) / 15 ( $S=100$ )	1e-4 ( $S=50$ ) / 5e-4 ( $S=100$ )
Box inpainting	0.2	25 ( $S=50$ ) / 25 ( $S=100$ )	0.0
Random inpainting	0.8	25 ( $S=50$ ) / 20 ( $S=100$ )	0.0
Gaussian deblur	0.5	25 ( $S=50$ ) / 25 ( $S=100$ )	0.0
Motion deblur	0.3	30 ( $S=50$ ) / 25 ( $S=100$ )	0.0

Appendix

Table 7: LEEGS training configuration for the noisy inverse problems (Tables 1 , 2 ).

Figure 5: Ground truth and the 5 noiseless inpainting mask operators used for Table 3 (CelebA-HQ example).

Mask	Learning rate $\eta$	Epochs	Weight decay
ImageNet
Wide	0.2	5	0.0
Narrow	0.2	5	0.0
Super-resolve ( $2\times$ )	0.2	5	0.0
Alternating lines	0.2	5	0.0
Half	0.2	5	0.0

Appendix

Table 8: LEEGS training configuration for image inpainting (Table 3 ).

NFEs	Learning rate $\eta$	Epochs	Weight decay
50	0.1	15	0.0
100	0.1	10	0.0

Appendix

Table 9: LEEGS training configuration for Face-ID guidance (Table 4 ).

Problem	Learning rate $\eta$	Epochs
Poisson, forward	15.0	15 ( $S=50$ ) / 15 ( $S=100$ )
Poisson, inverse	500.0	15 ( $S=50$ ) / 15 ( $S=100$ )
Helmholtz, forward	15.0 ( $S=50$ ) / 10.0 ( $S=100$ )	15 ( $S=50$ ) / 15 ( $S=100$ )
Helmholtz, inverse	1500.0	15 ( $S=50$ ) / 10 ( $S=100$ )
Darcy, forward	30.0	15 ( $S=50$ ) / 15 ( $S=100$ )
Darcy, inverse	150000.0 ( $S=50$ ) / 100000.0 ( $S=100$ )	15 ( $S=50$ ) / 15 ( $S=100$ )

Appendix

Table 10: LEEGS training configuration for the PDE problems (Table 5 ).

Results table	$S$	Epochs	Wall-clock	Time/epoch
FFHQ (Table 1 )	50	25 – 30	1h26m – 1h57m	3.4 – 3.9 min
FFHQ (Table 1 )	100	15 – 25	1h52m – 3h06m	7.5 min
ImageNet (Table 2 )	50	20	3h11m	9.6 min
ImageNet (Table 2 )	100	15	4h44m	19.0 min
Inpainting (Table 3 )	200 (CelebA-HQ)	5	3h13m	38.7 min
Inpainting (Table 3 )	200 (ImageNet)	5	3h14m	38.7 min

Appendix

Table 11: Training wall-clock time by results table and NFE budget

S

, on a single A100 GPU with no validation logging. Where tasks at a fixed

S

use different epoch counts, both the minimum and maximum are reported (as a range); a single value indicates every task at that

S

trains for the same number of epochs.

Figure 6: Held-out test-set reconstruction quality as a function of training dataset size

n

. Scatter points are the

10

individual dataset draws, and the vertical bar spans min to max, with the mean indicated by a red square. Left: FFHQ motion deblur. Right: Helmholtz forward.

Figure 7: Per-draw

L_{1}

distance of the learned guidance schedule from the draw-averaged schedule (all

S=10

steps), as a function of training dataset size

n

. Left: FFHQ motion deblur. Right: Helmholtz forward.

Figure 8: Draw-averaged guidance schedule (mean over

10

dataset draws) as a function of diffusion step, compared across training dataset sizes

n

Left: FFHQ motion deblur. Right: Helmholtz forward.

Figure 9: Learned guidance schedules for LEEGS and the true gradient (FFHQ and ImageNet motion deblur,

S=10

). Each panel shows the

10

per-draw schedules (thin grey) and their mean (bold); the true gradient’s higher spread on ImageNet is visible in the wider band around the mean, especially at later diffusion steps.

Dataset	Mode	LPIPS ( $\downarrow$ )	$L_{2}$ dist. from mean	$L_{1}$ dist. from mean
FFHQ	LEEGS	$0.341\pm 0.004$	$2.05$	$4.50$
FFHQ	True gradient	$0.342\pm 0.006$	$2.34$	$5.52$
ImageNet	LEEGS	$0.560\pm 0.007$	$2.28$	$5.13$
ImageNet	True gradient	$0.594\pm 0.041$	$7.03$	$17.89$

Appendix

Table 12: LEEGS vs. the true gradient on motion deblur (

S=10

; mean

\pm

std over

10

draws).

L_{1}

L_{2}

dist. from mean is each draw’s schedule distance to the

10

-draw mean. On ImageNet the true gradient is both worse and far less stable than LEEGS (std

4

–

6\times

higher on LPIPS, distances

\sim\!3\times

higher); on FFHQ the two are comparable.

Figure 10: Wall-clock cost per training iteration vs. inference budget

S

, for LEEGS and the true gradient, relative to plain sampling. Left: FFHQ box inpainting – true gradient

\approx 20\times

sampling, LEEGS

\approx 4\times

. Right: Helmholtz forward – true gradient

\approx 16\times

, LEEGS

\approx 4\times

Figure 11: Held-out LPIPS as a function of weight decay

\gamma

, one curve per

S

(discrete colorbar). Left: superresolution. Right: box inpainting.

Figure 12: Learned guidance schedules for the five FFHQ noisy inverse tasks against normalized diffusion time (

0

: noisiest,

1

: clean). Left: raw. Right: each schedule divided by its mean. Top:

S=50

. Bottom:

S=100

. The schedules differ strongly in magnitude and, to a lesser extent, in shape.

Panel of Figure 13 — Figure 13: Held-out LPIPS ( $300$ FFHQ images) when sampling with the schedule learned for the row task under the measurement operator of the column task. The best entry per column is in bold. Left: original schedules. Right: off-diagonal schedules rescaled to the mean guidance of the column task’s schedule. Top: $S=50$ . Bottom: $S=100$ . The matched schedule is best in almost every column before rescaling; after rescaling, some tasks continue to remain selective with respect to shape.

Figure 14: Mean guidance value of the trained schedules as a function of

S

, with the linear fit used for rescaling. Left: FFHQ box inpainting. Right: Helmholtz forward. The mean guidance decreases monotonically with

S

$S_{\text{src}}\to S_{\text{tgt}}$	Trained	Interp.	Interp.+rescale
$10\to 20$	0.217	0.203	0.204
$10\to 30$	0.173	0.169	0.170
$10\to 50$	0.140	0.142	0.139
$10\to 100$	0.119	0.156	0.113
$20\to 30$	0.173	0.172	0.174
$20\to 50$	0.140	0.139	0.140

Appendix

Table 13: FFHQ box inpainting: LPIPS (

\downarrow

) on

300

held-out samples. Bold : best of the three columns.

$S_{\text{src}}\to S_{\text{tgt}}$	Trained	Interp.	Interp.+rescale
$10\to 20$	11.70%	9.80%	10.01%
$10\to 30$	10.34%	9.13%	9.01%
$10\to 50$	9.33%	9.88%	8.73%
$10\to 100$	9.07%	15.05%	8.77%
$20\to 30$	10.34%	9.54%	9.77%
$20\to 50$	9.33%	9.09%	9.04%

Appendix

Table 14: Helmholtz forward: relative

L_{2}

error on

u

(%,

\downarrow

) on

300

held-out samples. Bold : best of the three columns.

Panel of Figure 15 — Figure 15: Training LPIPS vs. epoch, full vs. terminal-only constraint set, one panel per diffusion step budget $S$ .

Figure 16: Held-out LPIPS vs.

S

, full vs. terminal-only constraint set.

Subtask	Learning rate $\eta$	Epochs
Super-resolution ( $4\times$ )	0.3	15
Box inpainting	0.2	30
Random inpainting	0.8	30
Gaussian deblur	0.5	25
Motion deblur	0.3	15

Appendix

Table 15: LEEGS-renoise training configuration,

S=50

K=5

Task	LEEGS	LEEGS-renoise	Relative change
Box inpainting	0.174	0.165	$-5.2\%$
Random inpainting	0.196	0.181	$-7.5\%$
Gaussian deblur	0.243	0.246	$+1.3\%$
Motion deblur	0.212	0.227	$+7.0\%$
Superresolution	0.222	0.224	$+0.6\%$

Appendix

Table 16: LPIPS on the FFHQ test set (

950

images),

S=50

Panel of Figure 17 — Figure 17: Learned LEEGS-renoise guidance schedules for the five FFHQ tasks ( $S=50$ , $K=5$ ) against normalized diffusion time ( $0$ : noisiest, $1$ : clean); color indicates the outer step. Every outer step except the last has a hill shape.

Subtask	Learning rate $\eta$	Epochs
Super-resolution ( $4\times$ )	0.3	30
Box inpainting	0.2	20
Random inpainting	0.8	30
Gaussian deblur	0.3	20
Motion deblur	0.3	20

Appendix

Table 17: LEEGS training configuration for the

S=10

FFHQ extension (Table 18 ).

Figure 18: Box inpainting, FFHQ, $10$ NFEs.

Figure 19: Random inpainting, FFHQ, $10$ NFEs.

Figure 20: Superresolution ( $\times 4$ ), FFHQ, $10$ NFEs.

Figure 21: Gaussian deblur, FFHQ, $10$ NFEs.

Figure 22: Motion deblur, FFHQ, $10$ NFEs.

Dataset	NFEs	Wide	Narrow	S. res. (2x)	Alternate Lines	Half
Imagenet	200	0.0019	0.0040	0.0016	0.0018	0.0041
CelebA-HQ	200	0.0010	0.0001	0.0001	0.0005	0.0016

Appendix

Table 21: Standard deviation across 3 draws for the LEEGS rows of Table 3 (image inpainting).

NFEs	FaceID Score	FID
50	0.0036	0.90
100	0.0119	0.85

Appendix

Table 22: Standard deviation across 3 draws for the LEEGS rows of Table 4 (Face-ID guidance).

NFEs	Poisson		Helmholtz		Darcy
NFEs	Forward	Inverse	Forward	Inverse	Forward	Inverse
50x1	0.01%	0.06%	0.08%	0.25%	4.27%	1.54%
100x1	0.01%	0.19%	0.06%	0.18%	1.45%	5.28%

Appendix

Table 23: Standard deviation across 3 draws for the LEEGS rows of Table 5 (PDE problems).

Dataset	Method	NFEs	Wide	Narrow	S. res. (2x)	Alternate Lines	Half
Imagenet	LEEGS (ours)	200	0.0058	0.0045	0.0029	0.0020	0.0030
Imagenet	RePaint	200	0.0093	0.0075	0.0021	0.0079	0.0014
CelebA-HQ	LEEGS (ours)	200	0.0022	0.0011	0.0003	0.0002	0.0013
CelebA-HQ	RePaint	200	0.0053	0.0045	0.0023	0.0002	0.0017

Appendix

Table 30: Variance of LPIPS across test samples (

\downarrow

) for image inpainting. Green (bold): best.

Dataset	Method	NFEs	Wide	Narrow	S. res. (2x)	Alternate Lines	Half
Imagenet	LEEGS (ours)	200	20.28	24.20	27.76	29.74	13.71
Imagenet	RePaint	200	18.88	21.69	16.81	21.65	13.47
CelebA-HQ	LEEGS (ours)	200	24.99	29.00	32.76	35.00	16.41
CelebA-HQ	RePaint	200	21.40	24.73	29.24	36.46	13.88

Appendix

Table 31: PSNR in dB (

\uparrow

) for image inpainting. Green (bold): best.

Dataset	Method	NFEs	Wide	Narrow	S. res. (2x)	Alternate Lines	Half
Imagenet	LEEGS (ours)	200	0.777	0.808	0.834	0.880	0.594
Imagenet	RePaint	200	0.784	0.794	0.295	0.635	0.584
CelebA-HQ	LEEGS (ours)	200	0.879	0.917	0.941	0.964	0.720
CelebA-HQ	RePaint	200	0.847	0.868	0.845	0.966	0.670

Appendix

Table 32: SSIM (

\uparrow

) for image inpainting. Green (bold): best.

Figure 23: ImageNet. Left: raw. Right: mean-normalized. Top:

50

NFEs. Bottom:

100

NFEs.

Figure 24: Image inpainting,

200

NFEs. Left: raw. Right: mean-normalized. Top: CelebA-HQ. Bottom: ImageNet.

Figure 25: Face-ID guidance. Left: raw. Right: mean-normalized. Both NFE budgets overlaid.

Figure 26: Helmholtz and Poisson, forward. Left: raw. Right: mean-normalized. Top:

50

NFEs. Bottom:

100

NFEs.

Figure 27: Helmholtz and Poisson, inverse. Left: raw. Right: mean-normalized. Top:

50

NFEs. Bottom:

100

NFEs.

Figure 28: Darcy flow,

50

and

100

NFEs; raw and normalized within each panel. Top: forward. Bottom: inverse.

Figure 29: Constant guidance, FFHQ: LPIPS vs. guidance scale; best value in red.

Figure 30: Constant guidance, ImageNet: LPIPS vs. guidance scale; best value in red.

Figure 31: Linear increase, FFHQ: LPIPS vs. guidance scale; best value in red.

Figure 32: Linear increase, ImageNet: LPIPS vs. guidance scale; best value in red.

Figure 33: Linear decrease, FFHQ: LPIPS vs. guidance scale; best value in red.

Figure 34: Linear decrease, ImageNet: LPIPS vs. guidance scale; best value in red.

Figure 35: DSG, FFHQ: LPIPS vs. guidance scale; best value in red.

Figure 36: DSG, ImageNet: LPIPS vs. guidance scale; best value in red.

Figure 37: DAPS, FFHQ,

50

NFEs: LPIPS per configuration

(D,A)

; best value in orange.

Figure 38: DAPS, FFHQ,

100

NFEs: LPIPS per configuration

(D,A)

; best value in orange.

Figure 39: DAPS, ImageNet,

50

NFEs: LPIPS per configuration

(D,A)

; best value in orange.

Figure 40: DAPS, ImageNet,

100

NFEs: LPIPS per configuration

(D,A)

; best value in orange.

Figure 41: Constant guidance, FFHQ,

10

NFEs: LPIPS vs. guidance scale; best value in red.

Figure 42: Linear increase, FFHQ,

10

NFEs: LPIPS vs. guidance scale; best value in red.

Figure 43: DSG, FFHQ,

10

NFEs: LPIPS vs. guidance scale; best value in red.

Figure 44: DAPS, FFHQ,

10

NFEs: LPIPS per configuration

(D,A)

; best value in orange.

Figure 45: RePaint, CelebA-HQ: LPIPS per configuration

(S,N,J)

; best value in orange.

Figure 46: RePaint, ImageNet: LPIPS per configuration

(S,N,J)

; best value in orange.

Figure 47: Constant guidance, Face-ID (CelebA-HQ): FaceID score vs. guidance scale; columns:

S=50,100

; best value in red.

Figure 48: DSG, Face-ID (CelebA-HQ): FaceID score vs. guidance scale; columns:

S=50,100

; best value in red.

Figure 49: Constant guidance, Darcy: error vs. guidance scale; columns: forward/inverse

\times

{

50

100

NFEs}; best value in red.

Figure 50: Constant guidance, Poisson: as in Figure 49 .

Figure 51: Constant guidance, Helmholtz: as in Figure 49 .

Figure 52: Linear increase, Darcy: error vs. guidance scale; columns: forward/inverse

\times

{

50

100

NFEs}; best value in red.

Figure 53: Linear increase, Poisson: as in Figure 52 .

Figure 54: Linear increase, Helmholtz: as in Figure 52 .

Figure 55: Linear decrease, Darcy: as in Figure 52 .

Figure 56: Linear decrease, Poisson: as in Figure 52 .

Figure 57: Linear decrease, Helmholtz: as in Figure 52 .

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Diffusion models have achieved strong performance in image, text-to-image, and video generation, where conditional generation is often controlled by classifier-free guidance (CFG). CFG improves condition consistency by increasing a guidance weight, but stronger guidance typically reduces diversity and distributional coverage. It remains unclear how this consistency-coverage trade-off should be controlled across the reverse trajectory, since the distribution induced by CFG is not simply the fixed-time tilted distribution given by the guided score field. To address this issue, we propose an information-theoretic framework for CFG schedule optimization. Our approach uses a clean endpoint reference to specify the desired consistency-coverage trade-off, while optimizing the actual distribution induced by the guided sampler toward this reference. We derive trajectory-level formulas to estimate the objective from samples and score evaluations, avoiding explicit density estimation. On ImageNet-512 with EDM-XXL and COCO with SD-XL, the learned schedules achieve competitive or improved trade-offs over constant guidance and allocate guidance selectively across noise levels.

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