The paper investigates learning transition kernels for time‑homogeneous jump‑diffusion processes using conditional diffusion models, aiming to generate new sample paths from high‑frequency discrete observations. It provides non‑asymptotic bounds on conditional score estimation error and KL divergence between true and generated path distributions. Experiments on synthetic data validate the theory and compare favorably to Gao et al. (2025), while real‑world applications demonstrate its utility for probabilistic forecasting.
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.
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.
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.
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.
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.
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.
arXiv:2608. 14067v1 Announce Type: new Abstract: Diffusion models offer a natural way to model uncertainty in time series forecasting, yet their iterative sampling process is often treated as a uniformly beneficial refinement procedure.
arXiv:2609.28371v1 Announce Type: new Abstract: Generalized Langevin equations describe non-Markovian dynamics in which the evolution of resolved variables depends on their past. We propose a memory-...
arXiv:2607. 04780v1 Announce Type: cross Abstract: Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow.
arXiv:2606. 02232v1 Announce Type: new Abstract: Learning a Markov transition model is not merely conditional density estimation: the learned object must be a valid transition kernel before it is iterated in downstream dynamics.
arXiv:2609.09586v1 Announce Type: new Abstract: Time series foundation models (TSFMs) are increasingly pre-trained on synthetically generated time series trajectories, where the data generating proce...
arXiv:2411. 08314v5 Announce Type: replace Abstract: Learning to transform conditional probability densities over time is a fundamental challenge spanning probabilistic modeling and the natural sciences.