# Time-changed normalizing flows for accurate SDE modeling

arXiv: https://arxiv.org/abs/2312.14698 · HTML: https://mlsanity.com/paper/2312.14698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise](https://mlsanity.com/paper/1906.02355/) (2019)
- [Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows](https://mlsanity.com/paper/2002.10516/) (2020)
- [Latent SDEs on Homogeneous Spaces](https://mlsanity.com/paper/2306.16248/) (2023)
- [Continuous Latent Process Flows](https://mlsanity.com/paper/2106.15580/) (2021)
- [Learning Gradients of Convex Functions with Monotone Gradient Networks](https://mlsanity.com/paper/2301.10862/) (2023)
- [Point Process Flows](https://mlsanity.com/paper/1910.08281/) (2019)

## Abstract (arXiv)

The generative paradigm has become increasingly important in machine learning and deep learning models. Among popular generative models are normalizing flows, which enable exact likelihood estimation by transforming a base distribution through diffeomorphic transformations. Extending the normalizing flow framework to handle time-indexed flows gave dynamic normalizing flows, a powerful tool to model time series, stochastic processes, and neural stochastic differential equations (SDEs). In this work, we propose a novel variant of dynamic normalizing flows, a Time Changed Normalizing Flow (TCNF), based on time deformation of a Brownian motion which constitutes a versatile and extensive family of Gaussian processes. This approach enables us to effectively model some SDEs, that cannot be modeled otherwise, including standard ones such as the well-known Ornstein-Uhlenbeck process, and generalizes prior methodologies, leading to improved results and better inference and prediction capability.