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Parallel Sampling of Diffusion Models

Andy Shih, Suneel Belkhale, Stefano Ermon, Dorsa Sadigh, Nima Anari

arXiv:2305.16317v3cs.LGcs.AI

TL;DR

Diffusion models can require many sequential denoising steps, and reducing steps for speed can cost sample quality. ParaDiGMS parallelizes denoising with Picard iterations and works alongside existing samplers; across robotics and image-generation tasks, it reports 2–4x speedups without measurable quality degradation.

  • Problem

    Diffusion sampling can be slow, while reducing denoising steps to accelerate it can hurt sample quality.

    Source: §1 · p. 1

  • Method

    ParaDiGMS uses Picard iterations to guess and refine the denoising trajectory while computing multiple denoising steps in parallel.

    Source: §1 · p. 1, §3 · p. 3

  • Results

    Around 2–4x speedup across robotics and image-generation models, with no measurable decrease in task reward, FID score, or CLIP score.

    Source: §1 · p. 2, §5 · p. 10

  • Takeaways & Limitations

    The faster sampling speeds can support real-time execution of diffusion policies or interactive image generation.

    Source: §1 · p. 2

    ParaDiGMS increases model evaluations, so it is not suitable for users with limited compute who want to maximize sample throughput.

    Source: §5 · p. 9

Abstract

from arXiv · show

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 14.6s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

1 Introduction

Diffusion sampling can be slow, and reducing denoising steps to speed it up can cost sample quality. ParaDiGMS instead parallelizes denoising steps, achieving faster sampling without measurable quality loss across robotics and image-generation tasks.

1 Introduction

  • Reducing denoising steps is a common way to accelerate sampling, but it can come at the cost of sample quality.DDIM and DPMSolver are cited as examples of methods that reduce the number of steps.Source: §1 · p. 1
  • The paper asks whether additional parallel compute can speed up a single sample without reducing its number of denoising steps or sacrificing quality.Naïve parallelization improves throughput by generating multiple samples, but does not by itself address single-sample latency.Source: §1 · p. 1
  • ParaDiGMS parallelizes denoising through Picard iterations, guessing the full trajectory and refining it until convergence.The paper reports that convergence takes far fewer iterations than the number of denoising steps.Source: §1 · p. 1
  • ParaDiGMS is presented as the first general method to trade compute for sampling speed and is compatible with classifier-free guidance, DDIM, and DPMSolver.The authors describe combining it with prior samplers as an orthogonal way to trade both compute and quality for speed.Source: §1 · p. 2
  • Around 2–4x speedup across robotics and image-generation tasks and samplers, with no measurable decrease in task reward, FID score, or CLIP score.Examples include DiffusionPolicy action generation dropping from 0.74s to 0.2s and 1000-step StableDiffusion-v2 generation from 50.0s to 14.6s on A100 GPUs.Source: §1 · p. 2

2 Background

The background describes diffusion sampling as sequential denoising, with DDPMs represented both as discrete-time latent-variable models and through an SDE perspective. It then explains how lower-step samplers use an ODE formulation to make accelerated sampling more amenable to fewer steps.

2 Background

  • DDPMs use a discrete-time forward diffusion process from the data distribution toward a Gaussian prior, followed by sequential sampling with a learned reverse model.The reverse model is parameterized as a Gaussian and generates data by denoising one step at a time.Source: §2 · p. 2
  • The SDE view treats DDPM sampling as discretizing a reverse process whose drift is approximated by the inference model.The paper assumes access to the pretrained model's drift computation and notes that the SDE noise is position-independent.Source: §2 · p. 2

2.1 Reducing the number of denoising steps

  • DDPM typically uses 1000 sequential denoising steps, while DDIM and DPMSolver reduce steps to trade speed for quality.Directly reducing stochastic DDPM steps can significantly hurt quality; probability-flow ODE sampling is used to make low-step methods more amenable to preserving it.Source: §2.1 · pp. 2–3

3 Parallel computation of denoising steps

The section parallelizes denoising by using Picard iterations to refine a guessed trajectory, then implements the method with memory-aware sliding windows and compatibility with faster samplers.

3 Parallel computation of denoising steps

  • Picard iteration starts from a guessed ODE solution and repeatedly updates it toward the trajectory, converging to the unique solution under mild conditions on the drift.The stated conditions include continuity in time and Lipschitz continuity in position.Source: §3 · p. 3
  • Each iteration computes drift values in parallel and combines them with prefix sums, so sampling time can scale with convergence iterations K rather than denoising steps T.The update introduces skip dependencies: each timestep uses all previous timesteps rather than only its immediate predecessor.Source: §3 · p. 4
  • In practice, approximate convergence typically takes far fewer than T iterations, while exact convergence is guaranteed within K ≤ T iterations.After k iterations, the first k points match the sequential solution.Source: §3 · p. 4

3.1 Practical considerations

  • Mini-batching confines Picard iteration to a window of size p to manage GPU memory, and a sliding-window strategy advances once the window's starting timesteps converge.The algorithm checks errors to determine how far forward to shift the window.Source: §3.1 · pp. 4–5
  • For reverse SDE sampling, ParaDiGMS samples position-independent noise upfront and absorbs it into the drift, making the equation deterministic while retaining conditions that guarantee Picard convergence.The resulting equation is described as Lipschitz continuous in position and continuous in time.Source: §3.1 · p. 4
  • The section's stopping rule uses a low tolerance to keep parallel samples close to sequential sampling in total variation distance, under the stated linear-convergence assumption.The authors report reliable speedups without measurable quality degradation for a setting with τ = 0.1 and data dimensionality D.Source: §3.1 · p. 5
  • ParaDiGMS can replace Euler discretization with existing samplers such as DDIM and DPMSolver, combining fewer denoising steps with parallel computation.The passage also names higher-order methods such as Heun.Source: §3.1 · pp. 5–6

4 Experiments

Across robotic control and image-generation evaluations, ParaDiGMS speeds sampling relative to sequential baselines while maintaining measured sample quality.

4 Experiments

  • ParaDiGMS delivers around 2-4x speedup across robotic-control and image-generation tasks without measurable degradation in task reward, FID, or CLIP score.The evaluated models include Square, PushT, Franka Kitchen, StableDiffusion-v2, and LSUN Church and Bedroom.Source: §4 · p. 6

4.1 Diffusion policy

  • Square speedups are 3.7x, 1.6x, and 1.8x for ParaDDPM, ParaDDIM, and ParaDPMSolver without reward decrease; Kitchen ParaDDPM reaches 3.4x.In FrankaKitchen, episode rollout time falls from 112s to 33.3s.Source: §4.1 · pp. 6–7

4.2 Diffusion image generation

  • Image-generation experiments cover StableDiffusion-v2 in latent space and LSUN Church and Bedroom directly in pixel space.The evaluated StableDiffusion-v2 model uses a 4x96x96 latent space; the LSUN models use 3x256x256 pixel space.Source: §4.2 · p. 7

4.2.1 Latent-space diffusion models

  • With an 80-step batch window across 8 A100s, ParaDDPM exceeds 3x speedup, with 20x fewer parallel iterations than sequential steps.The net speedup balances extra model evaluations against hardware efficiency from batched multi-GPU execution.Source: §4.2.1 · pp. 7–8

4.2.2 Pixel-space diffusion models

  • On LSUN, ParaDiGMS yields over 3x speedup with multiple GPUs while maintaining baseline FID; 500-step DDIM has worse FID than 1000-step DDPM.The authors omit DPMSolver comparison because it was not yet integrated with the LSUN model.Source: §4.2.2 · pp. 8–9

4.3 Related work

  • Prior Picard-like parallel sampling work addressed log-concave and determinantal distributions; this work applies parallel sampling to diffusion models.The authors note that other higher-order ODE-based fast samplers should also be compatible, whereas distillation and learned samplers require additional training.Source: §4.3 · p. 9

5 Conclusion

ParaDiGMS trades additional computation for faster diffusion sampling and is compatible with existing sequential samplers. Its speedups come with increased model evaluations, making it a poor fit for compute-limited users seeking maximum throughput.

5 Conclusion

  • Because convergence requires more model evaluations than sequential sampling, ParaDiGMS is unsuitable for users with limited compute who want to maximize throughput.Source: §5 · p. 9
  • The compute-for-speed tradeoff fits interactive image generation, real-time robotic policies, and users insensitive to compute costs.Source: §5 · p. 10
  • ParaDiGMS approximates sequential samplers by iterating until errors fall below a tolerance, with no measurable quality degradation across tested tasks and metrics.On LSUN Church FID, ParaDDPM is reported to be both faster and higher-quality than 500-step DDIM.Source: §5 · p. 10
  • Around 2–4x speedup across robotics and image-generation models, without sacrificing sample quality, is the paper’s reported overall result.ParaDiGMS is compatible with sequential samplers such as DDIM and DPMSolver.Source: §5 · p. 10

A Proof of exact convergence

The proof of Proposition 1 begins with an induction assumption on xk+1.

A Proof of exact convergence

B Total variation analysis

The analysis bounds total variation error across denoising steps. It uses a per-step tolerance bound and shows that the accumulated final error is at most ϵ.

B Total variation analysis

  • A linear convergence rate with factor ≥2 bounds the error from the sequential-sampling solution by the chosen tolerance at each timestep.Source: B Total variation analysis · p. 13
  • The inference model samples from a Gaussian with variance σ²_t in the stepwise total-variation analysis.Source: B Total variation analysis · p. 13
  • The proof bounds the final sample-to-model total variation distance by ϵ using data processing and the triangle inequality.The per-step bound is ϵ/T, which accumulates over T timesteps.Source: B Total variation analysis · p. 13

C Parallel Computation on Multiple GPUs

The multi-GPU implementation uses multiprocessing rather than DataParallel, with one producer and multiple consumer processes. The producer runs the main loop while consumers execute model evaluations in parallel.

C Parallel Computation on Multiple GPUs

D.1 LSUN Church and LSUN Bedroom

The LSUN experiments plot ParaDDPM wall-clock speedup against batch window size and GPU count, showing a trend similar to StableDiffusion-v2. The plotted net speedup accounts for hardware efficiency and algorithm inefficiency.

D.1 LSUN Church and LSUN Bedroom

  • The LSUN experiments show a wall-clock speedup trend similar to StableDiffusion-v2 as batch window size and GPU count vary.The comparison concerns unconditional 256x256 LSUN Church and Bedroom generation with 1000-step ParaDDPM runs on A100 GPUs.Source: §D.1 · p. 14, Figure 5 · p. 14
  • Figure 5 reports net speedup after dividing hardware efficiency by algorithm inefficiency as batch window size increases.Its setup uses unconditional 256x256 images on LSUN Church and Bedroom, with 1000-step ParaDDPM on A100 GPUs.Source: Figure 5 · p. 14
  • Table 5 shows better speedups than Figure 5 because it uses multiprocessing instead of DataParallel.Source: Figure 5 · p. 14

D.2 Ablation

The tolerance ablation for 200-step ParaDDIM on StableDiffusion-v2 identifies τ=1e-1 as a good choice, balancing sampling speed and CLIP score.

D.2 Ablation

  • τ=1e-1 is a good tolerance choice for 200-step ParaDDIM on StableDiffusion-v2.Table 6 compares sample quality and speed; CLIP score uses 1000 samples and speed is measured on A100 GPUs.Source: §D.2 · p. 14, Table 6 · p. 14
  • Lower tolerance takes more parallel iterations and gives less speedup without a noticeable CLIP score increase.Source: §D.2 · p. 14
  • Higher tolerance advances the batch window more aggressively, reducing iterations and speeding sampling, but CLIP score drops.Source: §D.2 · p. 14
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