# Autoregressive One-Step Generative Modeling for Dynamical System Forecasting

arXiv: https://arxiv.org/abs/2605.05540 · HTML: https://mlsanity.com/paper/2605.05540/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 60 of its 80 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 60)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [SEINE: Short-to-Long Video Diffusion Model for Generative Transition and Prediction](https://mlsanity.com/paper/2310.20700/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [FIFO-Diffusion: Generating Infinite Videos from Text without Training](https://mlsanity.com/paper/2405.11473/) (2024)
- [AR-Diffusion: Auto-Regressive Diffusion Model for Text Generation](https://mlsanity.com/paper/2305.09515/) (2023)
- [Inductive Moment Matching](https://mlsanity.com/paper/2503.07565/) (2025)

## Abstract (arXiv)

Fast surrogate modeling for high-dimensional physical dynamics requires more than low short-term error: useful models must roll out efficiently while preserving the statistical structure of long trajectories. Neural operators provide inexpensive autoregressive forecasts but can drift in turbulent regimes, whereas rolling diffusion and latent generative surrogates can represent stochastic transitions at the cost of multi-step denoising, noise-schedule design, or auxiliary compression models. We propose MeanFlow Long-term Invariant Spatiotemporal Consistency Autoregressive Models (MeLISA), a latent-free autoregressive generative surrogate built on pixel-space MeanFlow. MeLISA defines a blockwise stochastic transition kernel that generates each forecast block with a single model evaluation, avoiding latent encoders and iterative diffusion solvers at inference time. To stabilize long-horizon rollouts, MeLISA combines a Window-Consistency MeanFlow objective that learns conditional spatiotemporal generation from partially observed temporal windows with a Time Increment Consistency loss that constrains multi-lag finite increments and targets temporal-correlation structure. We evaluate MeLISA with compact UNet and scalable DiT backbones on two high-resolution benchmarks, extended 2D Kolmogorov flow at 256 × 256 and turbulent channel-flow slice at 192 × 192. MeLISA outperforms neural-operator baselines on short-term forecasting accuracy and long-horizon statistical metrics, including energy spectra, turbulent kinetic energy, and mixing-rate-related dynamics, while achieving inference speeds comparable to, and in some cases faster than, neural operators. To our knowledge, this is the first method for high-resolution one-step generation for physical dynamical systems with performance comparable to state-of-the-art deterministic surrogates.