LatentFlow: A General Framework for Conditioning Stochastic Processes
arXiv:2607. 12922v1 Announce Type: cross Abstract: Stochastic-process models are, as a rule, far easier to simulate than to condition.
The paper introduces a new quasi‑stationarity diagnostic for accelerated dynamics methods, replacing traditional MCMC diagnostics with a coarse‑graining framework for killed Markov jump processes and a recurrent neural network trained on particle approximations of non‑linear effective flows. It provides uniform‑in‑time, non‑asymptotic bounds for approximating the true process’s probability flow without assuming reversibility, and demonstrates that the learned RNN diagnostic outperforms the MCMC approach in ROC analysis, is less conservative, fails less often, and offers an interpretable decision threshold.
arXiv:2607. 12922v1 Announce Type: cross Abstract: Stochastic-process models are, as a rule, far easier to simulate than to condition.
Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions.
arXiv:2606. 16219v1 Announce Type: cross Abstract: Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales can indefinitely increase model complexity, ultimately producing systems that are difficult to maintain, validate, interpret, and use for stress or safety testing.
arXiv:2604. 23952v2 Announce Type: replace-cross Abstract: Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging.
arXiv:2608.25631v1 Announce Type: cross Abstract: Continuous-time Markov chains (CTMCs) provide the backbone for modeling discrete stochastic dynamics across applied, physical, and biological science...
arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
The paper introduces latent jump models (LJMs) for continuous-time latent state-space modeling, where the latent state evolves deterministically between Poisson-driven events and experiences learned instantaneous jumps at each event. It presents a tractable event-augmented ELBO and a novel Scan-Parallel Variational Inference (SPVI) method that samples the full latent event configuration before evaluating state recurrence, enabling logarithmic temporal depth and fast, scalable training. Experiments on synthetic and real irregular time series show that LJMs achieve competitive forecast accuracy with fewer latent updates and train one to two orders of magnitude faster than sequential baselines.
arXiv:2508. 15318v5 Announce Type: replace-cross Abstract: Markov chain Monte Carlo (MCMC) is a standard tool for studying many-body systems, but its practical cost can become substantial, especially when simulations must be repeated across temperatures and lattice sizes or near transition regions where equilibration becomes increasingly difficult.
The paper introduces Critically‑Damped Higher‑Order Langevin Dynamics (C‑HOLD) for generative modeling, extending the concept of critical damping to arbitrary‑order Langevin dynamics. It builds on the recent Higher‑Order Langevin Dynamics (HOLD) method by providing an optimal hyperparameter set for the n‑dimensional case and closed‑form expressions for the mean and covariance of the forward process. Experiments on CIFAR‑10 and CelebA‑HQ 256×256 datasets demonstrate the approach’s effectiveness using the FID metric.
The paper introduces a scalable Bayesian method for conditional density estimation using a logistic Gaussian process. It models the log conditional density with a separable covariance— a Matérn kernel on the response dimension and a Nyström-feature kernel on covariates— and samples the latent field via kinetic Langevin dynamics instead of traditional approximations. Experiments on photometric‑redshift data with up to 3.9 million observations show the approach matches state‑of‑the‑art tabular foundation models on density and calibration metrics.
arXiv:2609.15894v1 Announce Type: cross Abstract: Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states cha...
The paper introduces an iterative neural variational solver for the committor function in under‑damped Langevin dynamics. By splitting the infinitesimal generator into self‑adjoint and skew‑adjoint parts, each subproblem gains a variational form that can be efficiently solved with neural networks, resembling a generalized Concus‑Golub‑Widlund splitting. The method is validated on benchmark systems such as a double‑well potential, the Muller‑Brown potential, and alanine dipeptide, demonstrating practical accuracy and extensibility for studying rare transition events across different damping coefficients.