arXiv research

This paper bridges the gap between ODE and SDE in diffusion models using Fokker-Planck equations.

Faster training of neural ODEs using Gauß-Legendre quadrature.

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…

Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.

Efficiently trains forward processes to minimize generative trajectories curvature.

AdjointDEIS simplifies diffusion model optimization.

Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE), usually rely on a completely deterministic feed-forward operation. This work pr…

A new sampling method called Restart improves both speed and quality of generative processes.

New error bounds for flow matching methods using deterministic sampling.

The paper examines the sampling dynamics of diffusion models using ODEs.

SA-Solver improves stochastic sampling from DPMs.

New method speeds up generative modeling without requiring diffusion steps.

This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit …

New estimator for SDEs is shown to be an adjoint state method.

In this paper we derive a scaling limit for an infinite dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator. With our choice of scaling the dynamics converges to a coupled SDE-ODE s…

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. …

Derives scaling limits and fluctuations for SGD in high dimensions.

Generative model uses SDEs to transform data distributions.

New theory improves diffusion model convergence for generating data.

There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of methods that are 'well-calibrated' in a specific sense. But the computational c…

GLASS Flows improves flow and diffusion model performance by optimizing sampling efficiency.

CT-OT Flow estimates continuous-time dynamics from discrete snapshots.

DDPM encoder matches optimal transport for natural images.

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated quantification of prediction uncertainty, while maintaining the expressive power …

New SDEs from affine and polynomial perspectives for path-dependent processes.

Improved analysis for diffusion models reduces KL divergence error dependence on data dimension and discretization step size.

SignSGD analysis quantifies its effects in high dimensions.

JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.

ML-EM method speeds up diffusion model sampling.

A novel score-based method solves high-dimensional Fokker-Planck equations with improved accuracy and speed.

We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from polytopes in R^n specified by m inequalities. The walk is a discrete-time simulation of a stochastic differential equation (SDE) on the Riemannian manifold equipped with the metric induc…

New theory improves diffusion models' convergence rates.

Reflected Diffusion Models improve on score-based models by incorporating data constraints.

We convert deterministic flow models to stochastic samplers.

The one-dimensional SDE with non Lipschitz diffusion coefficient $dX_{t} = b(X_{t})dt + σX_{t}^γ dB_{t}, \ X_{0}=x, \ γ<1$ is widely studied in mathematical finance. Several works have proposed asymptotic analysis of densities and implied volatilities in models involving instances of this equation, based on a careful i…

Stochastic differential equation approximation for linear TD(0) under Markovian noise

SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.

Consistency models accelerate generation with theoretical guarantees.

New SDEs use $G$-Brownian motion, extending mean-field models.

New SDE model for continuous-time reinforcement learning.

Sig-SDE model integrates signatures with SDEs for financial data.

Proposes neural SDEs with change points for better time series modeling.

TADA improves diffusion sampling without training, up to 186% faster.

Proposes methods to include distributional information in MV-SDEs for better modeling of interacting particle systems.

Neural SDEs model continuous sequences using neural networks.

Generates consistent IV surfaces using VAEs and SDE models.

New method speeds up SDE inference by matching moments to FPK equation.

TFM trains Neural SDEs without backpropagation, improving clinical time series modeling.