# Constrained Diffusion with Trust Sampling

arXiv: https://arxiv.org/abs/2411.10932 · HTML: https://mlsanity.com/paper/2411.10932/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 17 Nov 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Human Motion Diffusion Model](https://mlsanity.com/paper/2209.14916/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Action2Motion: Conditioned Generation of 3D Human Motions](https://mlsanity.com/paper/2007.15240/) (2020)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [EDGE: Editable Dance Generation From Music](https://mlsanity.com/paper/2211.10658/) (2022)
- [OmniControl: Control Any Joint at Any Time for Human Motion Generation](https://mlsanity.com/paper/2310.08580/) (2023)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Listen, Denoise, Action! Audio-Driven Motion Synthesis with Diffusion Models](https://mlsanity.com/paper/2211.09707/) (2022)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion](https://mlsanity.com/paper/2312.00852/) (2023)
- [Guidance with Spherical Gaussian Constraint for Conditional Diffusion](https://mlsanity.com/paper/2402.03201/) (2024)
- [MoDi: Unconditional Motion Synthesis from Diverse Data](https://mlsanity.com/paper/2206.08010/) (2022)

## Built on by (most cited first, 10 of 10)

- [Diffuse-CLoC: Guided Diffusion for Physics-based Character Look-ahead Control](https://mlsanity.com/paper/2503.11801/) (2025)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling](https://mlsanity.com/paper/2505.18017/) (2025)
- [RODS: Robust Optimization Inspired Diffusion Sampling for Detecting and Reducing Hallucination in Generative Models](https://mlsanity.com/paper/2507.12201/) (2025)
- [SPG: Improving Motion Diffusion by Smooth Perturbation Guidance](https://mlsanity.com/paper/2503.02577/) (2025)
- [Constrained Diffusion Models with Primal-Dual Inference](https://mlsanity.com/paper/2606.17192/) (2026)
- [Constraint-Guided Prediction Refinement via Deterministic Diffusion Trajectories](https://mlsanity.com/paper/2506.12911/) (2025)
- [Concept Guidance: Precise, Training-Free Latent Control for Text-to-Image Generation](https://mlsanity.com/paper/2608.14172/) (2026)
- [Self-Augmented Diffusion Guidance for Physics-Informed Generation](https://mlsanity.com/paper/2608.26748/) (2026)
- [Inference-Time Projection for Physically Valid Biomolecular Diffusion Models](https://mlsanity.com/paper/2610.07037/) (2026)

## Abstract (arXiv)

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion from an optimization perspective. We formulate a series of constrained optimizations throughout the inference process of a diffusion model. In each optimization, we allow the sample to take multiple steps along the gradient of the proxy constraint function until we can no longer trust the proxy, according to the variance at each diffusion level. Additionally, we estimate the state manifold of diffusion model to allow for early termination when the sample starts to wander away from the state manifold at each diffusion step. Trust sampling effectively balances between following the unconditional diffusion model and adhering to the loss guidance, enabling more flexible and accurate constrained generation. We demonstrate the efficacy of our method through extensive experiments on complex tasks, and in drastically different domains of images and 3D motion generation, showing significant improvements over existing methods in terms of generation quality. Our implementation is available at https://github.com/will-s-h/trust-sampling.