NSFs learn SDE transition laws for efficient sampling.
problem Efficiently sampling between arbitrary time points in SDEs.
method Conditional normalising flows with architectural constraints.
result Up to two orders of magnitude speed-ups at large time gaps.
TCNF models SDEs using time deformation of Brownian motion.
problem Modeling SDEs with existing methods.
method Time-changed normalizing flows (TCNF) based on time deformation of Brownian motion.
result Improved modeling of SDEs, including Ornstein-Uhlenbeck process.
SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.
problem Training Latent SDEs with adjoint sensitivity methods is computationally expensive and limited.
method SDE Matching, inspired by Score- and Flow Matching, eliminates simulation for training Latent SDEs.
result SDE Matching achieves performance comparable to adjoint sensitivity methods while reducing computational complexity.
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabl…
TFM trains Neural SDEs without backpropagation, improving clinical time series modeling.
problem Modeling irregularly sampled time series in medicine.
method Trajectory Flow Matching (TFM) using flow matching for generative modeling.
result TFM improves performance on clinical time series datasets.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
New method identifies drift and diffusivity from SDE marginals.
problem Challenging task to identify drift and diffusion from SDE population dynamics.
method Proposes nn-APPEX, a Schrodinger Bridge-based inference method.
result Gradient-flow drift and Brownian diffusivity jointly identifiable from marginals.
Paper introduces a differentially private generative model using gradient flow and sliced Wasserstein distance.
problem Protecting privacy in sensitive training data for generative models.
method Gradient flow in the space of probability measures, Gaussian-smoothed Sliced Wasserstein Distance, and numerical scheme for SDE.
result Demonstrates higher-fidelity data generation at low privacy budget compared to existing methods.
Novel method for SDE calibration from sparse data using neural flows.
problem Calibrating SDEs from sparse, noisy observations.
method Characterization of posterior SDE using neural networks trained to solve a PDE with multiplicative updates.
result Significant improvement in scalability and accuracy compared to classical methods.
Study of stochastic differential equations on non-compact manifolds, solving open problem on strong completeness.
problem Open problem on strong completeness of SDEs on non-compact spaces.
method Systematic study of stochastic differential equations, solving open problem on strong completeness.
result Existence of global smooth solution flow of SDEs on R^n, including substantial growth of coefficients.
Itô maps provide a method for any-step SDE integration.
problem Stochastic dynamics
method Itô map formulation
result Empirical results on synthetic and image-generation benchmarks
We explain how Itô Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be used to derive graphical representations of Itô SDEs. We show how jets can be used…
Proposes methods to include distributional information in MV-SDEs for better modeling of interacting particle systems.
problem Modeling the behavior of an infinite number of interacting particles with distributional information.
method Semi-parametric methods and estimators for MV-SDEs.
result Explicitly including distributional dependence improves performance in modeling temporal data with interaction.
Study market efficiency under partial information using SDEs and optimization.
problem Market efficiency under partial information constraints.
method McKean-Vlasov-type SDEs, Wasserstein barycenters, KL divergence, convex optimization, optimal control, nonlinear filtering.
result Convergence of reduced-information market price processes to true price process under increasing information flow.
New bounds for heavy-tailed SDEs without info-theory terms.
problem Understanding generalization of heavy-tailed stochastic optimization.
method Fractional Fokker-Planck equation to estimate entropy flows.
result High-probability bounds with better dimension dependence.
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using L2 loss and regularity conditions. New framework for Bayesian inference using neural Schrödinger-Föllmer flows.
problem Approximate Bayesian inference in large datasets.
method Stochastic control, Schrödinger bridges, SDE-based models.
result Advocates stochastic control as a finite time and low variance alternative to SGLD.
Neural SDEs model continuous sequences using neural networks.
problem Modeling continuous-time dynamics in sequence data.
method Interprets time-series as samples from a continuous dynamical system, parameterized by Neural SDE.
result Demonstrates superior performance in diverse sequence modeling tasks.
High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical me…
New method uses coupled SDEs to edit images with high fidelity and consistency.
problem Challenges in editing image content with text-to-image models.
method Using coupled stochastic differential equations to guide generative model sampling.
result Achieves high prompt fidelity and near-pixel-level consistency.
Efficiently trains forward processes to minimize generative trajectories curvature.
problem High curvature of generative trajectories slows down sampling speed.
method Trains forward process to minimize curvature without ODE/SDE simulation.
result Lower curvature than previous models, decreased sampling costs.
GLASS Flows improves flow and diffusion model performance by optimizing sampling efficiency.
problem Efficiency bottleneck in sampling Markov transitions for flow and diffusion models.
method Introduces GLASS Flows, a new sampling paradigm that simulates a 'flow matching model within a flow matching model' to sample Markov transitions efficiently.
result Eliminates the trade-off between stochastic evolution and efficiency in large-scale text-to-image models.
Unified framework for SDMs and GANs with improved sampling and quality.
problem Limitations of SDMs and GANs in achieving fast sampling and high sample quality.
method Introducing a novel SDE named DiffFlow to describe the learning dynamics of SDMs and GANs, and proving the asymptotic optimality and maximal likelihood training scheme.
result Unified framework allows smooth transition between SDMs and GANs with flexible trade-off between sample quality and speed.
In the paper [Probab. Theory Relat. Fields, 100 (1994) 417-428] Xue-Mei Li has shown that the moment stability of an SDE is closely connected with the topology of the underlying manifold. In particular, she gave sufficient condition on SDE on a manifold M under which the fundamental group π1M=0. We prove that in …
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process X(t) and a \emph{predictive mean-field} backward SDE (BSDE) in the unknowns Y(t),Z(t),K(t,⋅). The driver of …
AdjointDEIS simplifies diffusion model optimization.
problem Optimizing diffusion models with respect to a differentiable metric.
method Novel bespoke ODE solvers for continuous adjoint equations.
result Continuous adjoint equations simplify to a simple ODE, improving efficiency.
CT-OT Flow estimates continuous-time dynamics from discrete snapshots.
problem Estimating continuous-time dynamics from temporally aggregated snapshots with noisy or uncertain timestamps.
method Two-stage framework: aligning neighboring intervals via partial optimal transport (POT) and reconstructing a continuous-time distribution through temporal kernel smoothing.
result Reduces distributional and trajectory errors compared with existing methods across synthetic and real datasets.
A new framework models uncertainty in structured temporal data using SDEs and neural networks.
problem Uncertainty quantification in machine learning applications involving structured and temporal data.
method Integrates stochastic differential equations (SDEs) with deep generative models in a variational autoencoder framework.
result Improves uncertainty quantification in machine learning applications involving structured and temporal data.
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.
problem Efficiently simulating ergodic SDEs with large time-steps.
method Inference-based schemes adaptive to large time-steps (ISALT) from data.
result ISALT achieves significant time reduction and optimal accuracy.
Training-free model learns SDE dynamics without training, accelerating parameter studies.
problem High computational cost of simulating parameter-dependent SDEs.
method Training-free conditional diffusion model with joint kernel-weighted Monte Carlo estimator.
result Accurate approximation of conditional distributions across varying parameter values.
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. This work considers the diffusion limit of suc…
Unified ML approach for SDEs in bounded domains.
problem Challenges in simulating SDEs with particle exit phenomena.
method Hybrid approach combining diffusion model and exit prediction network.
result Accurate modeling of interior dynamics and boundary interactions.
New SDEs use G-Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G-SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
Modeling price impacts and trading signals for optimal execution and speculation.
problem Optimal execution and speculation in markets with trade signals.
method Price impact model driven by order flow, stochastic price impact, Meyer-σ-fields signal process, Marcus-type SDEs. result Derivation and numerical solution of HJB equation for optimal execution, enhanced speculative strategies.
New RDP guarantees for heavy-tailed SDEs and SGD.
problem Characterizing differential privacy for heavy-tailed noise in learning algorithms.
method Rényi flow computations and fractional Poincaré inequalities.
result First RDP guarantees for heavy-tailed SDEs with weaker dependence on dimension.
Study on stochastic mean curvature flow on networks using Ito calculus.
problem Understanding the dynamics of network structures under random influences.
method Application of Ito calculus to derive a stochastic differential equation (SDE) for network edges.
result New insights into the stability, long-term behavior, and pattern formation of complex networks under stochastic influences.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
Study on the smoothness of solutions to a specific type of stochastic differential equation.
problem Regularity of solutions to mean-field G-SDEs. method Analysis of first and second order Fréchet differentiability in the random initial condition.
result Established the Fréchet differentiability of the solution and specified the corresponding equations.
New method converts and optimizes sampling schedules for generative models.
problem Optimizing sampling schedules for generative models like flows and diffusions.
method Unified framework for stochastic interpolants, including point mass schedules.
result Demonstrated efficient generation of images with fewer steps.
New SDE model for continuous-time reinforcement learning.
problem Modeling exploration in continuous-time reinforcement learning.
method Introduced grid-sampling SDE as a proxy model.
result Wellposedness of the SDE in the presence of jumps.
GraphBSI generates graphs by refining a belief in continuous space, outperforming existing models.
problem Generating discrete, unordered graph data is challenging for traditional models.
method GraphBSI uses Bayesian Sample Inference (BSI) to iteratively refine a belief over graph distribution parameters.
result GraphBSI outperforms existing one-shot graph generative models on molecular and synthetic graph generation benchmarks.
This paper uses SDEs to analyze GANs training and long-run behavior.
problem Understanding the training process and long-run behavior of GANs.
method Established SDE approximations for GANs training and analyzed long-run behavior via invariant measures.
result The long-run behavior of GANs training can be studied via the invariant measures of its SDE approximations.
The paper identifies generators of linear SDEs with noise types.
problem Identifying the generator of linear SDEs from their solution distribution.
method Deriving sufficient and necessary conditions for additive noise, and sufficient conditions for multiplicative noise.
result Generic conditions for identifying the generator of linear SDEs with both types of noise.
Simulation-free VI closes the approximation gap in latent SDEs
problem Recovering dynamical systems from noisy observations
method Helmholtz-SDE
result Recovers dynamics more faithfully than prior methods
Sig-SDE model integrates signatures with SDEs for financial data.
problem Calibrating models to exotic financial products with non-linear dependencies.
method Integrating signatures from stochastic analysis with neural SDEs.
result Sig-SDE provides theoretical guarantees for convergence.
New method learns SDEs without integrators, speeding up computation.
problem Computational expense in learning SDEs using neural networks.
method Importance-sampling estimator for SDEs, leveraging parallelism.
result Lower-variance gradient estimates and massive computation time reductions.
New method speeds up SDE inference by matching moments to FPK equation.
problem Efficiency of sampling schemes in high-dimensional SDEs.
method Direct approximation of Fokker-Planck-Kolmogorov equation by matching moments.
result Fast, scalable inference in high-dimensional latent spaces.