arXiv:2608. 03117v1 Announce Type: new Abstract: The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions.
By Kentaro Kaba, Masayuki Ohzeki, Yuki Sughiyama
The paper investigates how repeatedly training score-based diffusion models on synthetic data can cause their outputs to drift from the target distribution. It provides theoretical upper and lower bounds on the divergence accumulated over successive training rounds, distinguishing regimes based on score estimation error and the fraction of fresh data used. Empirical experiments on synthetic data and images support the theoretical findings.
By Nail B. Khelifa, Richard E. Turner, Ramji Venkataramanan
The paper introduces block‑triangular joint drifting, a method that applies a projected drift field to the joint distribution of consecutive states, enabling one‑step generative surrogate models for stochastic transition dynamics. This architecture preserves the current‑state marginal while directly sampling the conditional distribution of next states, allowing stochastic trajectories to be generated with a single model evaluation per time step. Experiments show that the approach achieves accurate marginal and trajectory‑dependent statistics with favorable accuracy‑cost tradeoffs compared to deterministic, diffusion, flow, and distillation‑based generative surrogates.
By Nicholas Geissler, Shreya Jha, Ricardo Baptista, Benjamin Peherstorfer
arXiv:2508. 03636v3 Announce Type: replace-cross Abstract: We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion.
By Lei Qian, Wu Su, Yanqi Huang, Song Xi Chen
Spatial prediction is a key task in analyses of spatially or spatio-temporally referenced data, typically handled with hierarchical models that combine a process model and a data model. The predictive distribution—conditional on observed data—is often intractable, but guided diffusion modeling from machine learning can sample from it when the likelihood is known and differentiable. The authors demonstrate this approach on Gaussian and non‑Gaussian processes, various data models (direct observations, aggregates, counts, censoring, area‑exceedance), validate against exact and MCMC results, and apply it to methane‑flux inversion over the UK and Ireland, showing accurate sampling, applicability to intractable MCMC cases, and good scalability with dimensionality.
By Andrew Zammit-Mangion, Lachlan Astfalck, Rapha\"el Huser, Christopher Nemeth, Henry B. Moss
arXiv:2606. 30467v1 Announce Type: cross Abstract: We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data.
By Richard Schwank, Mathias Drton