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Constrained Diffusion with Trust Sampling
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Proposes Trust Sampling, a training-free loss-guided diffusion method that treats each diffusion step as a constrained optimization, taking multiple gradient steps on a proxy constraint loss until a variance-based trust schedule or a state-manifold noise-norm bound says to stop.
Problem
Training-free loss-guided diffusion struggles to satisfy challenging constraints, especially with small NFE budgets and when the one-step guidance proxy becomes unreliable at high-variance noise levels.
Approach
Reformulate each diffusion step's guidance as an iterative constrained optimization on a proxy loss, with the number of allowed gradient steps scheduled by a trust schedule tied to predicted-x0 variance and early termination when the predicted noise norm exceeds a state-manifold threshold.
Key results
- On FFHQ 256 super-resolution (4x), Trust reaches FID 16.99 and LPIPS 0.156 versus 29.48 / 0.212 for DPS (1000 NFEs).
- On ImageNet 256 super-resolution, Trust reaches FID 55.24 versus 111.53 for DPS and 108.00 for LGD-MC (n=100).
- Manifold boundary estimates reduce NFEs by 10-20% without substantial quality loss in image ablations; motion tasks showed no significant effect from the boundary.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Trust Sampling instead of DPS+DSG | Image restoration · FFHQ super-resolution, box inpainting, and Gaussian deblurring | FID: 29.48 -> 16.99; 18.92 -> 15.28; 24.06 -> 21.19 | Helped |
| Use Trust Sampling instead of DPS+DSG | Image restoration · ImageNet super-resolution, box inpainting, and Gaussian deblurring | LPIPS: 0.438 -> 0.236; 0.247 -> 0.210; 0.406 -> 0.266 | Helped |
| Use Trust Sampling instead of DPS | Motion generation · Root trajectory tracking | FID: 542.8 -> 561.6 | Hurt |
| Use Trust Sampling instead of DPS+DSG | Motion generation · Root trajectory tracking | Constraint violation (m): 0.022 -> 0.026 | Hurt |
| Use Trust Sampling instead of DPS+DSG | Motion generation · Root trajectory tracking | Diversity: 25.0 -> 21.5 | Helped |
| Use Trust Sampling instead of DPS | Motion generation · Right hand & left foot tracking | FID: 604.7 -> 694.1 | Hurt |
| Use Trust Sampling instead of DPS+DSG | Motion generation · Right hand & left foot tracking | Diversity: 24.0 -> 20.4 | Helped |
| Use Trust Sampling instead of DPS+DSG | Motion generation · Right hand & left foot tracking | Constraint violation (m): 0.035 -> 0.038 | Hurt |
| Use a non-constant linear schedule rather than a constant trust schedule (ablation) | Trust Sampling · FFHQ image restoration | FID: 36.95 -> 35.73; 34.72 -> 32.63; 47.25 -> 45.56 | Mixed |
| Reduce the inference budget from 1000 to 600 NFEs using start 0, end 4 schedule (ablation) | Trust Sampling · FFHQ image restoration | FID: 36.95 -> 34.94; 34.72 -> 38.70; 47.25 -> 48.94 | Mixed |
| Add manifold boundary estimates to trust scheduling (ablation) | Trust Sampling · FFHQ image restoration | FID: 34.94 -> 37.52; 38.70 -> 41.87; 48.94 -> 49.95 | Mixed |
| Vary εmax around 441.0 (ablation) | Trust Sampling · FFHQ super-resolution (×4) | FID: 50.81; 40.90; 35.85; 35.46; 36.06 | Mixed |
Surprising findings
- Manifold boundary estimates gave no significant effect on motion tasks.
- On motion tasks, DPS achieves the best FID (542.8 and 604.7), ahead of Trust, though with much higher constraint violation.
Limitations
- Relies on manually tuned heuristic parameters (trust schedule, epsilon_max) set per base model.
- Evaluation limited to 100-1000 validation images due to limited compute access.
- On motion tasks, DPS has better FID and DSG better constraint satisfaction.
Experimental setup
Datasets: FFHQ 256x256 ImageNet 256x256 AMASS
Benchmarks: FFHQ 256x256 linear inverse problems ImageNet 256x256 linear inverse problems AMASS-based motion constraint tasks
Metrics: FID LPIPS Diversity Constraint violation (m) NFEs
Baselines: DPS DPS+DSG LGD-MC
Builds on: DPS DDIM LGD-MC DSG EDGE
Closest papers by meaning
- CCS: Controllable and Constrained Sampling with Diffusion Models via Initial Noise Perturbation (NeurIPS 2025 · similarity 0.91)
- Fast constrained sampling in pre-trained diffusion models (NeurIPS 2025 · similarity 0.89)
- Constrained Diffusion Models via Dual Training (NeurIPS 2024 · similarity 0.89)
- Composition and Alignment of Diffusion Models using Constrained Learning (NeurIPS 2025 · similarity 0.89)
- A Simple Early Exiting Framework for Accelerated Sampling in Diffusion Models (ICML 2024 · similarity 0.89)
- Align Your Steps: Optimizing Sampling Schedules in Diffusion Models (ICML 2024 · similarity 0.89)
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