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Diffusion Models are Secretly Exchangeable: Parallelizing DDPMs via Auto Speculation

ICML 2025 · Image generation › Fast diffusion sampling · approach: Training-free diffusion acceleration

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Shows DDPM increments are exchangeable under a reparametrization to stochastic localization, and uses this to build Autospeculative Decoding, an error-free parallel sampler for DDPMs that uses the model itself as its draft.

Problem

DDPM sampling requires many sequential denoising steps (about 1000 for images, 100 for robot policies), creating an inference-time bottleneck; prior parallel methods rely on Picard iterations that leave approximation error or on restrictive Lipschitz assumptions.

Approach

Using the equivalence between DDPMs and stochastic localization, the paper proves that after a time/scale reparametrization the DDPM increments are exchangeable, so the current denoiser output can speculate future increments. Speculative decoding with Gaussian rejection sampling then verifies these speculations in parallel, with no draft model and exact output distribution.

Key results

• ASD on StableDiffusion-v2 reaches a peak wall-clock speedup of 1.82x (theta=6) on 8 A40 GPUs, with CLIP score unchanged (32.1 DDPM vs 32.0-32.3 ASD).
• On LSUN Church pixel diffusion, ASD reduces neural network calls by up to 3.1x, with FID matching DDPM (14.3).
• On Robomimic diffusion policies, ASD-infinity gives 6-7x algorithmic speedup and roughly 4x wall-clock speedup with success rates similar to DDPM.

Measured effects reported in the paper

Surprising findings

• The paper reports that the DDPM increments are exchangeable after reparametrization, a property it describes as hidden and not obvious, since the analogous property would fail for LLM token sequences.
• On the pixel-space LSUN model, the wall-clock gap is larger than the algorithmic gap because data transfer overhead between GPUs is about 10x higher, so wall-clock speedup lags algorithmic speedup.

Limitations

• Theoretical speedup guarantee assumes bounded second moments and step-size conditions; the bound is O~(K^{1/3}) speedup and depends on eta*d = O(1).
• Wall-clock speedups (1.8-4x) are well below the algorithmic speedups because of multi-GPU data transfer and batching overhead.
• Experiments cover only image generation and robot control; applicability to discrete diffusion (e.g., SEDD) is left to future work.

Experimental setup

Datasets: COCO2017 captions validation LSUN Church Robomimic

Benchmarks: COCO2017 captions (CLIP score) LSUN Church (FID) Robomimic Square Robomimic Transport Robomimic Tool Hang

Metrics: CLIP score FID success rate algorithmic speedup wall-clock speedup

Baselines: DDPM sequential sampling Picard iteration parallel sampling

Builds on: speculative decoding stochastic localization any-order autoregressive speculative decoding Picard iteration parallel sampling DDPM

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