# Variational Inference for L'evy Process-Driven SDEs via Neural Tilting

arXiv: https://arxiv.org/abs/2605.10934 · HTML: https://mlsanity.com/paper/2605.10934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 27 of 27)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Black-box Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/1802.03335/) (2018)
- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [Generative Fractional Diffusion Models](https://mlsanity.com/paper/2310.17638/) (2023)
- [Variational Inference for SDEs Driven by Fractional Noise](https://mlsanity.com/paper/2310.12975/) (2023)
- [Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals](https://mlsanity.com/paper/2405.13587/) (2024)
- [Extracting stochastic dynamical systems with α-stable L'evy noise from data](https://mlsanity.com/paper/2109.14881/) (2021)
- [Efficient Training of Neural SDEs Using Stochastic Optimal Control](https://mlsanity.com/paper/2505.17150/) (2025)
- [Fractional Diffusion Bridge Models](https://mlsanity.com/paper/2511.01795/) (2025)
- [On the exact and varepsilon-strong simulation of (jump) diffusions](https://mlsanity.com/paper/1302.6964/) (2013)
- [The L'evy State Space Model](https://mlsanity.com/paper/1912.12524/) (2019)
- [Generalised Hyperbolic State-space Models for Inference in Dynamic Systems](https://mlsanity.com/paper/2309.11422/) (2023)
- [Entropic Matching for Expectation Propagation of Markov Jump Processes](https://mlsanity.com/paper/2309.15604/) (2023)
- [Generalised shot noise representations of stochastic systems driven by non-Gaussian L'evy processes](https://mlsanity.com/paper/2305.05931/) (2023)

## Abstract (arXiv)

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While L'evy processes provide a natural mathematical framework for capturing jumps and heavy tails, Bayesian inference for L'evy-driven stochastic differential equations (SDEs) remains intractable with existing methods: Monte Carlo approaches are rigorous but lack scalability, whereas neural variational inference methods are efficient but rely on Gaussian assumptions that fail to capture discontinuities. We address this tension by introducing a neural exponential tilting framework for variational inference in L'evy-driven SDEs. Our approach constructs a flexible variational family by exponentially reweighting the L'evy measure using neural networks. This parametrization preserves the jump structure of the underlying process while remaining computationally tractable. To enable efficient inference, we develop a quadratic neural parametrization that yields closed-form normalization of the tilted measure, a conditional Gaussian representation for stable processes that facilitates simulation, and symmetry-aware Monte Carlo estimators for scalable optimization. Empirically, we demonstrate that the method accurately captures jump dynamics and yields reliable posterior inference in regimes where Gaussian-based variational approaches fail, on both synthetic and real-world datasets.