# Generative forecasting with joint probability models

arXiv: https://arxiv.org/abs/2512.24446 · HTML: https://mlsanity.com/paper/2512.24446/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [Analog forecasting of extreme-causing weather patterns using deep learning](https://mlsanity.com/paper/1907.11617/) (2019)
- [Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation](https://mlsanity.com/paper/2311.07896/) (2023)
- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos](https://mlsanity.com/paper/2503.18731/) (2025)
- [Long-term stability and generalization of observationally-constrained stochastic data-driven models for geophysical turbulence](https://mlsanity.com/paper/2205.04601/) (2022)
- [Generative Learning for Forecasting the Dynamics of Complex Systems](https://mlsanity.com/paper/2402.17157/) (2024)
- [Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows](https://mlsanity.com/paper/2512.09572/) (2025)
- [Uncertainty propagation in feed-forward neural network models](https://mlsanity.com/paper/2503.21059/) (2025)
- [Tensor rank reduction via coordinate flows](https://mlsanity.com/paper/2207.11955/) (2022)

## Built on by (most cited first, 2 of 2)

- [One-Step Generative Surrogate Models via Block-Triangular Joint Drifting](https://mlsanity.com/paper/2609.26435/) (2026)
- [AI Emulation of Stochastic Sudden Stratospheric Warming with Interpretable Latent Structure](https://mlsanity.com/paper/2610.02069/) (2026)

## Abstract (arXiv)

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by learning distributions over plausible system evolutions; yet, most existing approaches focus on next-step conditional prediction rather than the structure of the underlying dynamics. In this work, we reframe forecasting as a fully generative problem by learning the joint probability distribution of lagged system states over short temporal windows and obtaining forecasts through marginalization. This new perspective allows the model to capture nonlinear temporal dependencies, represent multistep trajectory segments, and produce next-step predictions consistent with the learned joint distribution. We also introduce a general, model-agnostic training and inference framework for joint generative forecasting and show how it enables assessment of forecast robustness and reliability using three complementary uncertainty quantification metrics (ensemble variance, short-horizon autocorrelation, and cumulative Wasserstein drift), without access to ground truth. We evaluate the performance of the proposed method on two canonical chaotic dynamical systems, the Lorenz-63 system and the Kuramoto-Sivashinsky equation, and show that joint generative models yield improved short-term predictive skill, preserve attractor geometry, and achieve substantially more accurate long-range statistical behaviour than conventional conditional next-step models.