# Fast Diffusion Model

arXiv: https://arxiv.org/abs/2306.06991 · HTML: https://mlsanity.com/paper/2306.06991/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 44 of its 52 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Placed in

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

## Builds on (most cited first, 30 of 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [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)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Text2Video-Zero: Text-to-Image Diffusion Models are Zero-Shot Video Generators](https://mlsanity.com/paper/2303.13439/) (2023)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)

## Built on by (most cited first, 21 of 21)

- [Consistent3D: Towards Consistent High-Fidelity Text-to-3D Generation with Deterministic Sampling Prior](https://mlsanity.com/paper/2401.09050/) (2024)
- [Boosting Diffusion Models with Moving Average Sampling in Frequency Domain](https://mlsanity.com/paper/2403.17870/) (2024)
- [Closed-Form Diffusion Models](https://mlsanity.com/paper/2310.12395/) (2023)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [A Closer Look at Time Steps is Worthy of Triple Speed-Up for Diffusion Model Training](https://mlsanity.com/paper/2405.17403/) (2024)
- [Diffusion Time-step Curriculum for One Image to 3D Generation](https://mlsanity.com/paper/2404.04562/) (2024)
- [Beta Diffusion](https://mlsanity.com/paper/2309.07867/) (2023)
- [Pruning then Reweighting: Towards Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2409.19128/) (2024)
- [Towards Faster Training of Diffusion Models: An Inspiration of A Consistency Phenomenon](https://mlsanity.com/paper/2404.07946/) (2024)
- [Doubly Abductive Counterfactual Inference for Text-based Image Editing](https://mlsanity.com/paper/2403.02981/) (2024)
- [Distilling ODE Solvers of Diffusion Models into Smaller Steps](https://mlsanity.com/paper/2309.16421/) (2023)
- [EVODiff: Entropy-aware Variance Optimized Diffusion Inference](https://mlsanity.com/paper/2509.26096/) (2025)
- [Adaptive Non-uniform Timestep Sampling for Accelerating Diffusion Model Training](https://mlsanity.com/paper/2411.09998/) (2024)
- [Learnable Sparsity for Vision Generative Models](https://mlsanity.com/paper/2412.02852/) (2024)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [Masked Diffusion Models Are Fast Distribution Learners](https://mlsanity.com/paper/2306.11363/) (2023)
- [Generative AI in Depth: A Survey of Recent Advances, Model Variants, and Real-World Applications](https://mlsanity.com/paper/2510.21887/) (2025)
- [Dreamguider: Improved Training free Diffusion-based Conditional Generation](https://mlsanity.com/paper/2406.02549/) (2024)
- [Diffusion Sampling with Momentum for Mitigating Divergence Artifacts](https://mlsanity.com/paper/2307.11118/) (2023)
- [DiFA: Inference-Time Forward-Process Alignment for Diffusion Models](https://mlsanity.com/paper/2607.17972/) (2026)
- [Consistent Distribution Matching for Data-Free Diffusion Distillation](https://mlsanity.com/paper/2610.09221/) (2026)

## Abstract (arXiv)

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.