# Immiscible Diffusion: Accelerating Diffusion Training with Noise Assignment

arXiv: https://arxiv.org/abs/2406.12303 · HTML: https://mlsanity.com/paper/2406.12303/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 18 Jun 2024.

## Placed in

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

## Builds on (most cited first, 30 of 36)

- [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)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Emergent Correspondence from Image Diffusion](https://mlsanity.com/paper/2306.03881/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Zero-Shot Robotic Manipulation with Pretrained Image-Editing Diffusion Models](https://mlsanity.com/paper/2310.10639/) (2023)
- [Diffusion Hyperfeatures: Searching Through Time and Space for Semantic Correspondence](https://mlsanity.com/paper/2305.14334/) (2023)
- [The Role of ImageNet Classes in Fr'echet Inception Distance](https://mlsanity.com/paper/2203.06026/) (2022)
- [Consistency Policy: Accelerated Visuomotor Policies via Consistency Distillation](https://mlsanity.com/paper/2405.07503/) (2024)
- [Hyper-SD: Trajectory Segmented Consistency Model for Efficient Image Synthesis](https://mlsanity.com/paper/2404.13686/) (2024)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)

## Built on by (most cited first, 14 of 14)

- [DexGraspVLA: A Vision-Language-Action Framework Towards General Dexterous Grasping](https://mlsanity.com/paper/2502.20900/) (2025)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [RealisDance-DiT: Simple yet Strong Baseline towards Controllable Character Animation in the Wild](https://mlsanity.com/paper/2504.14977/) (2025)
- [FlashAudio: Rectified Flows for Fast and High-Fidelity Text-to-Audio Generation](https://mlsanity.com/paper/2410.12266/) (2024)
- [DiverseFlow: Sample-Efficient Diverse Mode Coverage in Flows](https://mlsanity.com/paper/2504.07894/) (2025)
- [TPDiff: Temporal Pyramid Video Diffusion Model](https://mlsanity.com/paper/2503.09566/) (2025)
- [Improved Immiscible Diffusion: Accelerate Diffusion Training by Reducing Its Miscibility](https://mlsanity.com/paper/2505.18521/) (2025)
- [CoVAE: Consistency Training of Variational Autoencoders](https://mlsanity.com/paper/2507.09103/) (2025)
- [NoiseRater: Meta-Learned Noise Valuation for Diffusion Model Training](https://mlsanity.com/paper/2605.08144/) (2026)
- [One-Sided Quantile Coupling for Flow Matching](https://mlsanity.com/paper/2608.00978/) (2026)
- [Na"ive PAINE: Lightweight Text-to-Image Generation Improvement with Prompt Evaluation](https://mlsanity.com/paper/2603.12506/) (2026)
- [Can We Change the Stroke Size for Easier Diffusion?](https://mlsanity.com/paper/2603.26783/) (2026)
- [Noise in Diffusion Models Is a Learnable Input](https://mlsanity.com/paper/2608.02575/) (2026)
- [AVTR-1: Open Stack for Real-Time Interactive Avatars](https://mlsanity.com/paper/2609.22913/) (2026)

## Abstract (arXiv)

In this paper, we point out that suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscibility phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of molecular sources is distinguishable. Inspired by this concept, we propose an assignment-then-diffusion training strategy to achieve Immiscible Diffusion. As one example, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to expel the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. In this way, each image is preferably projected to nearby noise. Experiments demonstrate that our method can achieve up to 3x faster training for unconditional Consistency Models on the CIFAR dataset, as well as for DDIM and Stable Diffusion on CelebA and ImageNet dataset, and in class-conditional training and fine-tuning. In addition, we conducted a thorough analysis that sheds light on how it improves diffusion training speed while improving fidelity. The code is available at https://yhli123.github.io/immiscible-diffusion