# Infinite-Resolution Integral Noise Warping for Diffusion Models

arXiv: https://arxiv.org/abs/2411.01212 · HTML: https://mlsanity.com/paper/2411.01212/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 28 of its 50 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [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)
- [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)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [AnimateDiff: Animate Your Personalized Text-to-Image Diffusion Models without Specific Tuning](https://mlsanity.com/paper/2307.04725/) (2023)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generators](https://mlsanity.com/paper/2303.13439/) (2023)
- [ControlVideo: Training-free Controllable Text-to-Video Generation](https://mlsanity.com/paper/2305.13077/) (2023)
- [Pix2Video: Video Editing using Image Diffusion](https://mlsanity.com/paper/2303.12688/) (2023)
- [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023)
- [TEXTure: Text-Guided Texturing of 3D Shapes](https://mlsanity.com/paper/2302.01721/) (2023)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [EDICT: Exact Diffusion Inversion via Coupled Transformations](https://mlsanity.com/paper/2211.12446/) (2022)
- [FLATTEN: optical FLow-guided ATTENtion for consistent text-to-video editing](https://mlsanity.com/paper/2310.05922/) (2023)
- [ConsistI2V: Enhancing Visual Consistency for Image-to-Video Generation](https://mlsanity.com/paper/2402.04324/) (2024)
- [Self-Rectifying Diffusion Sampling with Perturbed-Attention Guidance](https://mlsanity.com/paper/2403.17377/) (2024)
- [Diffusion Handles: Enabling 3D Edits for Diffusion Models by Lifting Activations to 3D](https://mlsanity.com/paper/2312.02190/) (2023)
- [Generative Rendering: Controllable 4D-Guided Video Generation with 2D Diffusion Models](https://mlsanity.com/paper/2312.01409/) (2023)
- [Blue noise for diffusion models](https://mlsanity.com/paper/2402.04930/) (2024)
- [Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Models](https://mlsanity.com/paper/2410.16152/) (2024)
- [Cinemo: Consistent and Controllable Image Animation with Motion Diffusion Models](https://mlsanity.com/paper/2407.15642/) (2024)
- [Geometry-Aware Score Distillation via 3D Consistent Noising and Gradient Consistency Modeling](https://mlsanity.com/paper/2406.16695/) (2024)

## Built on by (most cited first, 5 of 5)

- [Go-with-the-Flow: Motion-Controllable Video Diffusion Models Using Real-Time Warped Noise](https://mlsanity.com/paper/2501.08331/) (2025)
- [Versatile Transition Generation with Image-to-Video Diffusion](https://mlsanity.com/paper/2508.01698/) (2025)
- [On Equivariance and Fast Sampling in Video Diffusion Models Trained with Warped Noise](https://mlsanity.com/paper/2504.09789/) (2025)
- [STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priors](https://mlsanity.com/paper/2504.07549/) (2025)
- [Phi-Noise: Training-Free Temporal Video Conditioning via Phase-Based Noise Manipulation](https://mlsanity.com/paper/2605.24509/) (2026)

## Abstract (arXiv)

Adapting pretrained image-based diffusion models to generate temporally consistent videos has become an impactful generative modeling research direction. Training-free noise-space manipulation has proven to be an effective technique, where the challenge is to preserve the Gaussian white noise distribution while adding in temporal consistency. Recently, Chang et al. (2024) formulated this problem using an integral noise representation with distribution-preserving guarantees, and proposed an upsampling-based algorithm to compute it. However, while their mathematical formulation is advantageous, the algorithm incurs a high computational cost. Through analyzing the limiting-case behavior of their algorithm as the upsampling resolution goes to infinity, we develop an alternative algorithm that, by gathering increments of multiple Brownian bridges, achieves their infinite-resolution accuracy while simultaneously reducing the computational cost by orders of magnitude. We prove and experimentally validate our theoretical claims, and demonstrate our method's effectiveness in real-world applications. We further show that our method readily extends to the 3-dimensional space.