arXiv:2606. 18071v1 Announce Type: cross Abstract: Score-based diffusion models typically use Brownian perturbations, which provide tractable reverse-time dynamics but impose memoryless noising.
arXiv:2601. 21868v2 Announce Type: replace-cross Abstract: Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning.
arXiv:2608. 02799v1 Announce Type: cross Abstract: Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus.
arXiv:2608. 10384v1 Announce Type: new Abstract: This paper studies inverse sampling for L\'evy-driven generative models from the perspective of Markov generators.
arXiv:2606. 15048v1 Announce Type: new Abstract: Diffusion models are typically trained with objectives that focus on local denoising targets at individual time steps (or adjacent pairs), which do not enforce consistency between predictions along the denoising trajectory.
We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure.
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
arXiv:2607. 08757v1 Announce Type: cross Abstract: Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory.
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:2605. 19805v2 Announce Type: replace-cross Abstract: Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift.
arXiv:2606. 13796v1 Announce Type: cross Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution.
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. This paper develops a non-asymptotic error analysis for such SMC samplers.
arXiv:2607. 10067v1 Announce Type: new Abstract: While autoregressive models optimize the exact data likelihood via the chain rule, diffusion models are typically trained with denoising objectives.