A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models

• URL: http://arxiv.org/abs/2608.19504v1
• Date: Wed, 19 Aug 2026 23:45:05 GMT
• Title: A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models
• Abstract summary: We propose a conditioning mechanism for diffusion models based on multi-speed joint diffusion of the target and the condition.<n>The mechanism learns an unconditional joint score network and enforces conditioning at inference via a plug-in correction term.<n>We derive explicit conditional reverse-time SDEs and approximate probability-flow ODEs, enabling principled and directly comparable conditional samplers.
• Score: 18.321591924290967
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a conditioning mechanism for diffusion models based on multi-speed joint diffusion of the target and the condition. The mechanism learns an unconditional joint score network and enforces conditioning at inference via a plug-in correction term. The plug-in term separates the conditioning contribution from the learned unconditional dynamics, offering a transparent view of how the condition steers generation of the target distribution. Building on this, we derive explicit conditional reverse-time SDEs and approximate probability-flow ODEs, enabling principled and directly comparable conditional samplers. To reduce the induced ODE--SDE discrepancy, we introduce a log-Fokker--Planck residual regularization that improves ODE sampling quality. Experiments on conditional image generation tasks demonstrate competitive performance and support the effectiveness of the plug-in conditioning view. Additional ODE--SDE comparison experiments show that the log-Fokker--Planck residual regularization improves deterministic ODE sampling.

Related papers

• Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory [2.148615003900331]
  We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients.<n>Experiments on static and time-dependent benchmark PDEs demonstrate competitive accuracy and faster inference than diffusion-based generative models.
  arXiv  Detail & Related papers  (2026-05-25T07:14:11Z)
• Condition Errors Refinement in Autoregressive Image Generation with Diffusion Loss [56.120591983649824]
  We present a theoretical analysis of diffusion and autoregressive models with diffusion loss.<n>We show that patch denoising optimization in autoregressive models effectively mitigates condition errors and leads to a stable condition distribution.<n>We introduce a novel condition refinement approach based on Optimal Transport (OT) theory to address condition inconsistency''
  arXiv  Detail & Related papers  (2026-02-02T07:48:04Z)
• Non-asymptotic error bounds for probability flow ODEs under weak log-concavity [6.661419982187023]
  This work establishes non-asymptotic convergence bounds in the 2-Wasserstein distance for a general class of probability flow ODEs.<n>Our results extend convergence theory to more realistic data distributions and practical ODE solvers.
  arXiv  Detail & Related papers  (2025-10-20T14:54:38Z)
• 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)
• Distilling Diffusion Models into Conditional GANs [90.76040478677609]
  We distill a complex multistep diffusion model into a single-step conditional GAN student model. For efficient regression loss, we propose E-LatentLPIPS, a perceptual loss operating directly in diffusion model's latent space. We demonstrate that our one-step generator outperforms cutting-edge one-step diffusion distillation models.
  arXiv  Detail & Related papers  (2024-05-09T17:59:40Z)
• Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory [87.00653989457834]
  Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. Despite the empirical success, theory of conditional diffusion models is largely missing. This paper bridges the gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models.
  arXiv  Detail & Related papers  (2024-03-18T17:08:24Z)
• Conditional Stochastic Interpolation for Generative Learning [10.187337578238063]
  We propose a conditional conditional (CSI) method for learning conditional distributions.<n>We derive explicit expressions of the conditional drift and score functions in terms of conditional expectations.<n>We illustrate the application of CSI on image generation using a benchmark image dataset.
  arXiv  Detail & Related papers  (2023-12-09T13:53:35Z)
• Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation [6.2255027793924285]
  The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of differential equations (SDEs) in machine learning. We demonstrate the theoretical guarantees of the model, the benefits of using Lipschitz networks for score matching, and its potential applications in various areas such as diffusion inversion, conditional diffusion, and uncertainty quantification.
  arXiv  Detail & Related papers  (2023-04-26T01:15:35Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Comparing Probability Distributions with Conditional Transport [63.11403041984197]
  We propose conditional transport (CT) as a new divergence and approximate it with the amortized CT (ACT) cost. ACT amortizes the computation of its conditional transport plans and comes with unbiased sample gradients that are straightforward to compute. On a wide variety of benchmark datasets generative modeling, substituting the default statistical distance of an existing generative adversarial network with ACT is shown to consistently improve the performance.
  arXiv  Detail & Related papers  (2020-12-28T05:14:22Z)

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.