arXiv 8 Jan 2026 · Statistics — Machine Learning
arXiv:2601.05227 · PDF · DOI · OpenAlex · Extracted main text
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach, termed Stochastic Latent Differential Inference (SLDI), embeds an Itô SDE in the latent space of a variational autoencoder, allowing for flexible, continuous-time modeling of uncertainty while preserving a principled mathematical foundation. The drift and diffusion terms of the SDE are parameterized by neural networks, enabling data-driven inference and generalizing classical time series models to handle irregular sampling and complex dynamic structure. A central theoretical contribution is the co-parameterization of the adjoint state with a dedicated neural network, forming a coupled forward-backward system that captures not only latent evolution but also gradient dynamics. I introduce a pathwise-regularized adjoint loss and analyze variance-reduced gradient flows through the lens of stochastic calculus, offering new tools for improving training stability in deep latent SDEs. My paper unifies and extends variational inference, continuous-time generative modeling, and control-theoretic optimization, providing a rigorous foundation for future developments in stochastic probabilistic machine learning.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kingma, Diederik P and Welling, Max (2013) Auto-Encoding Variational Bayes | 1.000 | 7 | 3 | 100% |
| 2 | Kidger, Patrick and Morrill, James and Foster, James and Lyons, Terry (2021) Neural SDEs as Infinite-Dimensional GANs | 1.000 | 5 | 4 | 100% |
| 3 | Chen, Ricky T. Q. and Rubanova, Yulia and Bettencourt, Jesse and Duv… (2018) Neural Ordinary Differential Equations | 1.000 | 5 | 3 | 100% |
| 4 | Archambeau, Cédric and Opper, Manfred (2011) Approximate Inference for Continuous-Time Markov Processes | 0.811 | 4 | 2 | 100% |
| 5 | Li, Xuechen and Wong, Ting-Kam Leonard and Chen, Ricky TQ and Duvena… (2020) Scalable Gradients for Stochastic Differential Equations | 0.811 | 4 | 2 | 100% |
| 6 | Pavliotis, Grigorios A (2014) Stochastic Processes and Applications: Diffusion Processes, the Fokker–Planck and Langevin Equations | 0.811 | 4 | 2 | 100% |
| 7 | Wang, Shengbo and Blanchet, Jose and Glynn, Peter (2024) An Efficient High-dimensional Gradient Estimator for Stochastic Differential Equations | 0.644 | 2 | 2 | 100% |
| 8 | Archer, Evan and Bayer, John and Koster, Ulrich and Duh, Kevin and B… (2015) Black Box Variational Inference for State Space Models | 0.644 | 2 | 2 | 100% |
| 9 | Kloeden, Peter E and Platen, Eckhard (1992) Numerical Solution of Stochastic Differential Equations | 0.644 | 2 | 2 | 100% |
| 10 | Miyato, Takeru and Kataoka, Toshiki and Koyama, Masanori and Yoshida… (2018) Spectral Normalization for Generative Adversarial Networks | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 46 scored citations.