Xiao Xue

Xiao Xue, Tianyue Yang, Mingyang Gao et al.

Spatiotemporal flows govern diverse phenomena across physics, biology, and engineering, yet modelling their multiscale dynamics remains a central challenge. Despite major advances in physics-informed machine learning, existing approaches struggle to simultaneously maintain long-term temporal evolution and resolve fine-scale structure across chaotic, turbulent, and physiological regimes. Here, we introduce Uni-Flow, a unified autoregressive-diffusion framework that explicitly separates temporal evolution from spatial refinement for modelling complex dynamical systems. The autoregressive component learns low-resolution latent dynamics that preserve large-scale structure and ensure stable long-horizon rollouts, while the diffusion component reconstructs high-resolution physical fields, recovering fine-scale features in a small number of denoising steps. We validate Uni-Flow across canonical benchmarks, including two-dimensional Kolmogorov flow, three-dimensional turbulent channel inflow generation with a quantum-informed autoregressive prior, and patient-specific simulations of aortic coarctation derived from high-fidelity lattice Boltzmann hemodynamic solvers. In the cardiovascular setting, Uni-Flow enables task-level faster than real-time inference of pulsatile hemodynamics, reconstructing high-resolution pressure fields over physiologically relevant time horizons in seconds rather than hours. By transforming high-fidelity hemodynamic simulation from an offline, HPC-bound process into a deployable surrogate, Uni-Flow establishes a pathway to faster-than-real-time modelling of complex multiscale flows, with broad implications for scientific machine learning in flow physics.

Tianyue Yang, Sandro Tacchella, Xiao Xue

Understanding galaxy morphology evolution across cosmic time requires models that can generate realistic galaxy populations conditioned on redshift. In this work, we study efficient redshift-conditioned generative modeling for astrophysical image synthesis using diffusion models and pixel-MeanFlow. We first review the connections between score-based diffusion models, Flow Matching, one-step generative models, and modern diffusion samplers. We then evaluate DDPM, DDIM, DEIS-AB2, DPM++2M, and one-step pixel-MeanFlow on the GalaxiesML-64 dataset using morphology-based metrics, including ellipticity, semi-major axis, Sérsic index, and isophotal area. Our results show a clear accuracy-efficiency trade-off: standard DDPM sampling achieves the best distributional fidelity but requires high computational cost, while second-order samplers substantially improve efficiency over DDIM. Pixel-MeanFlow enables single-step generation and achieves competitive performance on several morphology statistics, though it remains weaker than many-step DDPM for fine-grained structure. Our results demonstrate that one-step generative models can recover key galaxy morphology statistics at orders-of-magnitude lower computational cost, opening a path toward efficient conditional simulators for large cosmological surveys and simulation-based scientific inference.

Tianyue Yang, Xiao Xue

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 $256 \times 256$ and turbulent channel-flow slice at $192 \times 192$. 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. Compact 3.7-5.7M-parameter variants already deliver strong parameter efficiency, and DiT variants provide a scalable path up to 150M parameters. Overall, MeLISA benefits both rollout efficiency and long-horizon statistical accuracy.