Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps

• URL: http://arxiv.org/abs/2602.12624v1
• Date: Fri, 13 Feb 2026 05:02:07 GMT
• Title: Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps
• Authors: Sangwoo Jo, Sungjoon Choi,
• Abstract summary: Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs.<n>We propose SDM, a principled framework that aligns the numerical solver with the intrinsic properties of the diffusion trajectory.<n>By analyzing the ODE dynamics, we show that efficient low-order solvers suffice in early high-noise stages while higher-order solvers can be progressively deployed to handle the increasing non-linearity of later stages.
• Score: 4.397130429878499
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers, the holistic design of sampling, specifically solver selection and scheduling, remains dominated by static heuristics. In this work, we revisit this challenge through a geometric lens, proposing SDM, a principled framework that aligns the numerical solver with the intrinsic properties of the diffusion trajectory. By analyzing the ODE dynamics, we show that efficient low-order solvers suffice in early high-noise stages while higher-order solvers can be progressively deployed to handle the increasing non-linearity of later stages. Furthermore, we formalize the scheduling by introducing a Wasserstein-bounded optimization framework. This method systematically derives adaptive timesteps that explicitly bound the local discretization error, ensuring the sampling process remains faithful to the underlying continuous dynamics. Without requiring additional training or architectural modifications, SDM achieves state-of-the-art performance across standard benchmarks, including an FID of 1.93 on CIFAR-10, 2.41 on FFHQ, and 1.98 on AFHQv2, with a reduced number of function evaluations compared to existing samplers. Our code is available at https://github.com/aiimaginglab/sdm.

Related papers

• Dual-End Consistency Model [41.982957134224904]
  Slow iterative sampling is a major bottleneck for the practical deployment of diffusion and flow-based generative models.<n>We propose a Dual-End Consistency Model (DE-CM) that selects vital sub-trajectory clusters to achieve stable and effective training.<n>Our method achieves a state-of-the-art FID score of 1.70 in one-step generation on the ImageNet 256x256 dataset, outperforming existing CM-based one-step approaches.
  arXiv  Detail & Related papers  (2026-02-11T11:51:01Z)
• Parallel Diffusion Solver via Residual Dirichlet Policy Optimization [88.7827307535107]
  Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature.<n>Existing solver-based acceleration methods often face significant image quality degradation under a low-dimensional budget.<n>We propose the Ensemble Parallel Direction solver (dubbed as EPD-EPr), a novel ODE solver that mitigates these errors by incorporating multiple gradient parallel evaluations in each step.
  arXiv  Detail & Related papers  (2025-12-28T05:48:55Z)
• Model-Based Diffusion Sampling for Predictive Control in Offline Decision Making [48.998030470623384]
  offline decision-making requires reliable behaviors from fixed datasets without further interaction.<n>We propose a compositional model-based diffusion framework consisting of: (i) a planner that generates diverse, task-aligned trajectories; (ii) a dynamics model that enforces consistency with the underlying system dynamics; and (iii) a ranker module that selects behaviors aligned with the task objectives.
  arXiv  Detail & Related papers  (2025-12-09T06:26:02Z)
• Inference-Time Scaling of Diffusion Language Models with Particle Gibbs Sampling [70.8832906871441]
  We study how to steer generation toward desired rewards without retraining the models.<n>Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement.<n>We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity.
  arXiv  Detail & Related papers  (2025-07-11T08:00:47Z)
• Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpening [10.23957420290553]
  We propose the Optimal Transport Flow Matching framework to achieve one-step, high-quality pansharpening.<n>The OTFM framework enables simulation-free training and single-step inference while maintaining strict adherence to pansharpening constraints.
  arXiv  Detail & Related papers  (2025-03-19T08:10:49Z)
• A First-order Generative Bilevel Optimization Framework for Diffusion Models [57.40597004445473]
  Diffusion models iteratively denoise data samples to synthesize high-quality outputs.<n>Traditional bilevel methods fail due to the infinite-dimensional probability space and prohibitive sampling costs.<n>We formalize this challenge as a generative bilevel optimization problem.<n>Our first-order bilevel framework overcomes the incompatibility of conventional bilevel methods with diffusion processes.
  arXiv  Detail & Related papers  (2025-02-12T21:44:06Z)
• Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence [19.484676783876306]
  Diffusion models have emerged as powerful tools for generative modeling.<n>We propose a control framework for fine-tuning diffusion models.<n>We show that PI-FT achieves global convergence at a linear rate.
  arXiv  Detail & Related papers  (2024-12-24T04:55:46Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
  Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. We introduce a novel generative modeling framework grounded in textbfphase space dynamics Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
  arXiv  Detail & Related papers  (2023-10-11T18:38:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.