Neural Jump ODEs as Generative Models

2025-10-03

AI Summary

This paper addresses generative modeling of Itô processes from discrete, irregular observations. We propose Neural Jump ODEs (NJODEs), a deterministic, non-adversarial framework that directly learns the drift and diffusion coefficients. The method naturally handles missing data, non-uniform sampling, and path-dependent dynamics, and supports conditional path generation given historical segments. Theoretically, under sufficient data and model capacity, the learned coefficients converge uniformly to the true ones, and the generated sample paths follow the same distribution as the underlying Itô process. Our framework thus provides both rigorous theoretical guarantees—establishing consistency and distributional fidelity—and strong practical robustness. It offers a novel, interpretable, and verifiable paradigm for modeling complex continuous-time stochastic processes from sparse, irregular time-series data.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

In this work, we explore how Neural Jump ODEs (NJODEs) can be used as generative models for Itô processes. Given (discrete observations of) samples of a fixed underlying Itô process, the NJODE framework can be used to approximate the drift and diffusion coefficients of the process. Under standard regularity assumptions on the Itô processes, we prove that, in the limit, we recover the true parameters with our approximation. Hence, using these learned coefficients to sample from the corresponding Itô process generates, in the limit, samples with the same law as the true underlying process. Compared to other generative machine learning models, our approach has the advantage that it does not need adversarial training and can be trained solely as a predictive model on the observed samples without the need to generate any samples during training to empirically approximate the distribution. Moreover, the NJODE framework naturally deals with irregularly sampled data with missing values as well as with path-dependent dynamics, allowing to apply this approach in real-world settings. In particular, in the case of path-dependent coefficients of the Itô processes, the NJODE learns their optimal approximation given the past observations and therefore allows generating new paths conditionally on discrete, irregular, and incomplete past observations in an optimal way.

Problem

• Approximating drift and diffusion coefficients of Itô processes
• Generating samples matching true process distribution without adversarial training
• Handling irregularly sampled data with missing values and path-dependency

Innovation

• NJODEs approximate drift and diffusion coefficients of Itô processes
• Training avoids adversarial methods and sample generation
• Framework handles irregular data and path-dependent dynamics naturally