# Accelerating Parallel Sampling of Diffusion Models

arXiv: https://arxiv.org/abs/2402.09970 · HTML: https://mlsanity.com/paper/2402.09970/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 37 of its 57 references that are in the map.
- First posted on arXiv 15 Feb 2024.

## Placed in

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

## Builds on (most cited first, 30 of 37)

- [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)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [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)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Structure and Content-Guided Video Synthesis with Diffusion Models](https://mlsanity.com/paper/2302.03011/) (2023)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023)
- [Optimizing Prompts for Text-to-Image Generation](https://mlsanity.com/paper/2212.09611/) (2022)
- [SpecTr: Fast Speculative Decoding via Optimal Transport](https://mlsanity.com/paper/2310.15141/) (2023)
- [Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2305.16317/) (2023)
- [VMT-Adapter: Parameter-Efficient Transfer Learning for Multi-Task Dense Scene Understanding](https://mlsanity.com/paper/2312.08733/) (2023)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving](https://mlsanity.com/paper/2002.03629/) (2020)
- [Generative Text-Guided 3D Vision-Language Pretraining for Unified Medical Image Segmentation](https://mlsanity.com/paper/2306.04811/) (2023)

## Built on by (most cited first, 30 of 30)

- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)
- [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Efficient Diffusion Models: A Survey](https://mlsanity.com/paper/2502.06805/) (2025)
- [Accelerated Diffusion Models via Speculative Sampling](https://mlsanity.com/paper/2501.05370/) (2025)
- [Real-Time Pill Identification for the Visually Impaired Using Deep Learning](https://mlsanity.com/paper/2405.05983/) (2024)
- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Generalised Flow Maps for Few-Step Generative Modelling on Riemannian Manifolds](https://mlsanity.com/paper/2510.21608/) (2025)
- [SparseDiT: Token Sparsification for Efficient Diffusion Transformer](https://mlsanity.com/paper/2412.06028/) (2024)
- [Learning to Integrate Diffusion ODEs by Averaging the Derivatives](https://mlsanity.com/paper/2505.14502/) (2025)
- [Research on the Application of Computer Vision Based on Deep Learning in Autonomous Driving Technology](https://mlsanity.com/paper/2406.00490/) (2024)
- [DC-Gen: Post-Training Diffusion Acceleration with Deeply Compressed Latent Space](https://mlsanity.com/paper/2509.25180/) (2025)
- [Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations](https://mlsanity.com/paper/2412.08292/) (2024)
- [Predictability Enables Parallelization of Nonlinear State Space Models](https://mlsanity.com/paper/2508.16817/) (2025)
- [Adaptive Spectral Feature Forecasting for Diffusion Sampling Acceleration](https://mlsanity.com/paper/2603.01623/) (2026)
- [DA-VAE: Plug-in Latent Compression for Diffusion via Detail Alignment](https://mlsanity.com/paper/2603.22125/) (2026)
- [A Unifying Framework for Parallelizing Sequential Models with Linear Dynamical Systems](https://mlsanity.com/paper/2509.21716/) (2025)
- [Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling](https://mlsanity.com/paper/2607.00773/) (2026)
- [Mitigating the Contractivity Trap in Diffusion ODEs via Stein Stabilization](https://mlsanity.com/paper/2606.07835/) (2026)
- [PCM : Picard Consistency Model for Fast Parallel Sampling of Diffusion Models](https://mlsanity.com/paper/2503.19731/) (2025)
- [Accelerating Speculative Diffusions via Block Verification](https://mlsanity.com/paper/2606.13426/) (2026)
- [Accelerating Diffusion Sampling via Speculative Draft Trees](https://mlsanity.com/paper/2609.17691/) (2026)
- [TransTARec: Time-Adaptive Translating Embedding Model for Next POI Recommendation](https://mlsanity.com/paper/2404.07096/) (2024)
- [CHORDS: Diffusion Sampling Accelerator with Multi-core Hierarchical ODE Solvers](https://mlsanity.com/paper/2507.15260/) (2025)
- [K-Forcing: Joint Next-K-Token Decoding via Push-Forward Language Modeling](https://mlsanity.com/paper/2606.10820/) (2026)
- [You Only Look One Step: Accelerating Backpropagation in Diffusion Sampling with Gradient Shortcuts](https://mlsanity.com/paper/2505.07477/) (2025)
- [Switching Linear Attention](https://mlsanity.com/paper/2609.39034/) (2026)
- [Rank-Aware Speculative Sampling for Diffusion Draft Trees](https://mlsanity.com/paper/2610.02251/) (2026)

## Abstract (arXiv)

Diffusion models have emerged as state-of-the-art generative models for image generation. However, sampling from diffusion models is usually time-consuming due to the inherent autoregressive nature of their sampling process. In this work, we propose a novel approach that accelerates the sampling of diffusion models by parallelizing the autoregressive process. Specifically, we reformulate the sampling process as solving a system of triangular nonlinear equations through fixed-point iteration. With this innovative formulation, we explore several systematic techniques to further reduce the iteration steps required by the solving process. Applying these techniques, we introduce ParaTAA, a universal and training-free parallel sampling algorithm that can leverage extra computational and memory resources to increase the sampling speed. Our experiments demonstrate that ParaTAA can decrease the inference steps required by common sequential sampling algorithms such as DDIM and DDPM by a factor of 4~14 times. Notably, when applying ParaTAA with 100 steps DDIM for Stable Diffusion, a widely-used text-to-image diffusion model, it can produce the same images as the sequential sampling in only 7 inference steps. The code is available at https://github.com/TZW1998/ParaTAA-Diffusion.