Based onourformulation, weproposeDPM-Solver,afastdedicated high-order solver for diffusion ODEs with the convergence order guarantee.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works.

Our calibration method is performed only once and the resulting models can be used repeatedly for sampling.

Sec. 3.2, the only approximation of the proposed DPM-Solver is about the Taylor expansion of the

We introduce PINGS (Physics-Informed Neural Network for Fast Generative Sampling), a framework that amortizes diffusion sampling by training a physics-informed network to approximate reverse-time probability-flow dynamics, reducing sampling to a single forward pass (NFE = 1). As a proof of concept, we learn a direct map from a 3D standard normal to a non-Gaussian Gaussian Mixture Model (GMM). PINGS preserves the target's distributional structure (multi-bandwidth kernel $MMD^2 = 1.88 \times 10^{-2}$ with small errors in mean, covariance, skewness, and excess kurtosis) and achieves constant-time generation: $10^4$ samples in $16.54 \pm 0.56$ millisecond on an RTX 3090, versus 468-843 millisecond for DPM-Solver (10/20) and 960 millisecond for DDIM (50) under matched conditions. We also sanity-check the PINN/automatic-differentiation pipeline on a damped harmonic oscillator, obtaining MSEs down to $\mathcal{O}(10^{-5})$. Compared to fast but iterative ODE solvers and direct-map families (Flow, Rectified-Flow, Consistency), PINGS frames generative sampling as a PINN-style residual problem with endpoint anchoring, yielding a white-box, differentiable map with NFE = 1. These proof-of-concept results position PINGS as a promising route to fast, function-based generative sampling with potential extensions to scientific simulation (e.g., fast calorimetry).

Diffusion probabilistic models (DPMs) have achieved impressive success in visual generation. While, they suffer from slow inference speed due to iterative sampling. Employing fewer sampling steps is an intuitive solution, but this will also introduces discretization error. Existing fast samplers make inspiring efforts to reduce discretization error through the adoption of high-order solvers, potentially reaching a plateau in terms of optimization. This raises the question: can the sampling process be accelerated further? In this paper, we re-examine the nature of sampling errors, discerning that they comprise two distinct elements: the widely recognized discretization error and the less explored approximation error. Our research elucidates the dynamics between these errors and the step by implementing a dual-error disentanglement strategy. Building on these foundations, we introduce an unified and training-free acceleration framework, DualFast, designed to enhance the speed of DPM sampling by concurrently accounting for both error types, thereby minimizing the total sampling error. DualFast is seamlessly compatible with existing samplers and significantly boost their sampling quality and speed, particularly in extremely few sampling steps. We substantiate the effectiveness of our framework through comprehensive experiments, spanning both unconditional and conditional sampling domains, across both pixel-space and latent-space DPMs.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works.

Diffusion models have emerged as preeminent contenders in the realm of generative models. Distinguished by their distinctive sequential generative processes, characterized by hundreds or even thousands of timesteps, diffusion models progressively reconstruct images from pure Gaussian noise, with each timestep necessitating full inference of the entire model. However, the substantial computational demands inherent to these models present challenges for deployment, quantization is thus widely used to lower the bit-width for reducing the storage and computing overheads. Current quantization methodologies primarily focus on model-side optimization, disregarding the temporal dimension, such as the length of the timestep sequence, thereby allowing redundant timesteps to continue consuming computational resources, leaving substantial scope for accelerating the generative process. In this paper, we introduce TMPQ-DM, which jointly optimizes timestep reduction and quantization to achieve a superior performance-efficiency trade-off, addressing both temporal and model optimization aspects. For timestep reduction, we devise a non-uniform grouping scheme tailored to the non-uniform nature of the denoising process, thereby mitigating the explosive combinations of timesteps. In terms of quantization, we adopt a fine-grained layer-wise approach to allocate varying bit-widths to different layers based on their respective contributions to the final generative performance, thus rectifying performance degradation observed in prior studies. To expedite the evaluation of fine-grained quantization, we further devise a super-network to serve as a precision solver by leveraging shared quantization results. These two design components are seamlessly integrated within our framework, enabling rapid joint exploration of the exponentially large decision space via a gradient-free evolutionary search algorithm.