# Fast constrained sampling in pre-trained diffusion models

arXiv: https://arxiv.org/abs/2410.18804 · HTML: https://mlsanity.com/paper/2410.18804/

## 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 38 of its 52 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [SmartBrush: Text and Shape Guided Object Inpainting with Diffusion Model](https://mlsanity.com/paper/2212.05034/) (2022)

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

- [ZoomLDM: Latent Diffusion Model for multi-scale image generation](https://mlsanity.com/paper/2411.16969/) (2024)
- [PixCell: A generative foundation model for digital histopathology images](https://mlsanity.com/paper/2506.05127/) (2025)
- [Mitigating Diffusion Model Hallucinations with Dynamic Guidance](https://mlsanity.com/paper/2510.05356/) (2025)
- [Constrained Flow Optimization via Sequential Fine Tuning for Molecular Design](https://mlsanity.com/paper/2605.30610/) (2026)
- [Poppy: Polarization-based Plug-and-Play Guidance for Enhancing Monocular Normal Estimation](https://mlsanity.com/paper/2603.27891/) (2026)
- [Stochastic Transition-Map Distillation for Fast Probabilistic Inference](https://mlsanity.com/paper/2605.07661/) (2026)
- [Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping](https://mlsanity.com/paper/2605.27990/) (2026)
- [On the spectral properties of generative denoiser Jacobians](https://mlsanity.com/paper/2609.36210/) (2026)
- [Moore, Escher, Penrose: A Conformal Golden Braid](https://mlsanity.com/paper/2610.02210/) (2026)
- [BigCell: Generating Gigapixel Whole-Slide Images](https://mlsanity.com/paper/2610.14261/) (2026)

## Abstract (arXiv)

Large denoising diffusion models, such as Stable Diffusion, have been trained on billions of image-caption pairs to perform text-conditioned image generation. As a byproduct of this training, these models have acquired general knowledge about image statistics, which can be useful for other inference tasks. However, when confronted with sampling an image under new constraints, e.g. generating the missing parts of an image, using large pre-trained text-to-image diffusion models is inefficient and often unreliable. Previous approaches either utilized backpropagation through the denoiser network, making them significantly slower and more memory-demanding than simple text-to-image generation, or only enforced the constraint locally, failing to capture critical long-range correlations in the sampled image. In this work, we propose an algorithm that enables fast, high-quality generation under arbitrary constraints. We show that in denoising diffusion models, we can employ an approximation to Newton's optimization method that allows us to speed up inference and avoid the expensive backpropagation operations. Our approach produces results that rival or surpass the state-of-the-art training-free inference methods while requiring a fraction of the time. We demonstrate the effectiveness of our algorithm under both linear (inpainting, super-resolution) and non-linear (style-guided generation) constraints. An implementation is provided at https://github.com/cvlab-stonybrook/fast-constrained-sampling.