Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approach

TL;DR

The paper challenges the belief that faster diffusion sampling must come from higher-order solvers, showing that where and how DPM evaluations are placed can significantly impact accuracy at low NFEs. It introduces a training-free, first-order forward-value sampler that uses a cheap one-step lookahead to form a next-state estimate and then blends ${\bm \mu}_{\theta}(\widehat{\bm x}_{t_i},t_i)$ with the current state, achieving an $O(1/M)$ discretization error similar to DDIM. The authors prove convergence guarantees that the forward-value approach tracks the forward trajectory with first-order accuracy and demonstrate, across CIFAR-10, ImageNet, FFHQ, and LSUN, substantial sample-quality gains at the same NFE budgets, often matching or surpassing higher-order methods. These results reveal that the placement of DPM evaluations constitutes a meaningful, largely orthogonal design knob for accelerating diffusion sampling with practical impact in real-world generation tasks.

Abstract

Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is the primary path to faster generation. This paper challenges this belief and revisits acceleration from a complementary angle: beyond solver order, the placement of DPM evaluations along the reverse-time dynamics can substantially affect sampling accuracy in the low-neural function evaluation (NFE) regime. We propose a novel training-free, first-order sampler whose leading discretization error has the opposite sign to that of DDIM. Algorithmically, the method approximates the forward-value evaluation via a cheap one-step lookahead predictor. We provide theoretical guarantees showing that the resulting sampler provably approximates the ideal forward-value trajectory while retaining first-order convergence. Empirically, across standard image generation benchmarks (CIFAR-10, ImageNet, FFHQ, and LSUN), the proposed sampler consistently improves sample quality under the same NFE budget and can be competitive with, and sometimes outperform, state-of-the-art higher-order samplers. Overall, the results suggest that the placement of DPM evaluations provides an additional and largely independent design angle for accelerating diffusion sampling.

Figures (8)

• Figure 1: Qualitative comparisons between our sampler and DDIM, DPMSolver-2, DPMSolver-3, and UniPC-3. Images are sampled from pre-trained EDM2 with S and L size on ImageNet64 dataset.
• Figure 2: Qualitative comparisons between our sampler and DDIM, DPMSolver-2, DPMSolver-3, and UniPC-3. Images are sampled from pre-trained EDM2 with XS and XXL size on ImageNet512 dataset.
• Figure 3: Qualitative comparisons between our sampler and DDIM, DPMSolver-2, DPMSolver-3, and UniPC-3. Images are sampled from pre-trained latent diffusion model on FFHQ dataset.
• Figure 4: Qualitative comparisons between our sampler and DDIM, DPMSolver-2, DPMSolver-3, and UniPC-3. Images are sampled from pre-trained unconditional EDM on CIFAR10 dataset.
• Figure 5: Qualitative comparisons between our sampler and DDIM, DPMSolver-2, DPMSolver-3, and UniPC-3. Images are sampled from pre-trained conditional EDM on CIFAR10 dataset.