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.
Partial differential equations (PDEs) govern the spatiotemporal evolution of many dynamical systems central to science and engineering. From canonical problems in fluid dynamics to physiologically critical processes such as cardiovascular flows 1 , these systems often exhibit nonlinear, turbulent, and chaotic behaviour 2 . Accurately capturing and computing such dynamics across disparate temporal and spatial scales is essential for advancing both fundamental understanding and practical applications 3 . Traditionally, PDEs are solved numerically using finite difference 4 , finite volume 5 , and finite element 6 discretisations, which have enabled decades of progress in computational physics and engineering. Despite these advances, resolving multiscale dynamics remains computationally prohibitive, increasingly relying on exascale computing resources 7 and facing fundamental challenges arising from the simultaneous presence of long-term evolution and fine-scale structure 8 . In computational fluid dynamics (CFD), large eddy simulation (LES) [9][10][11] mitigates some of this cost by filtering unresolved small-scale motions. However, LES remains prohibitively expensive for many academic and industrial applications due to the fine grid resolution required near solid boundaries 12 , limiting its practicality for inverse design 13 and time-sensitive simulations. These computational constraints are particularly restrictive in physiological flow modelling, where high-fidelity solvers remain largely confined to offline analysis. Scientific machine learning (SciML) has emerged as a promising paradigm for accelerating the modelling of PDE-governed systems by learning their evolution directly from data 14 . Recent advances have demonstrated substantial speedups in simulating complex dynamical systems 15,16 , especially in regimes where traditional solvers are computationally demanding. Rather than discarding physical structure, physics-informed machine learning (PIML) incorporates conservation laws 17,18 , symmetries 19 , and governing equations into the learning process, ensuring physical consistency while leveraging the expressive capacity of modern machine learning models. Within CFD, machine learning has been applied to enhance PDE modelling through subgrid-scale closures 20,21 and turbulence modelling [22][23][24][25] , where resolving all flow scales is impractical. Reinforcement learning has been used to adaptively tune closure terms [26][27][28] , while physics-informed neural networks embed PDE residuals directly into loss functions 17 . These approaches reflect a broader trend toward hybridising data-driven learning with numerical solvers, allowing machine learning models to respect governing physical constraints.
Beyond targeted model enhancement, recent work has focused on learning the spatiotemporal evolution of entire fields. Recurrent neural architectures 29 , such as long short-term memory (LSTM) networks 30 , capture temporal dependencies but often struggle with long-horizon stability. Neural operator frameworks, including the Fourier Neural Operator 15 and DeepONet 31 , provide a general approach for learning mappings between infinite-dimensional function spaces, enabling efficient solutions of parametric PDEs. Despite their promise, most autoregressive and operator-learning models suffer from longterm instability, where accumulated errors degrade physical realism or cause predictions to collapse towards trivial states. Efforts to stabilise chaotic dynamics through invariantmeasure preservation and constrained learning [32][33][34] have largely been limited to simplified or low-resolution systems. Despite these advances, in general, such approaches have struggled to preserve the correct macroscopic dynamics, with machine-learned surrogate models often diverging from the true long-term behaviour 35 .
A complementary line of work has explored diffusion models [36][37][38] for reconstructing high-resolution physical fields. Originally developed for image synthesis and restoration 39 , diffusion models have demonstrated strong performance in recovering fine-scale structure and multiscale features in complex flows 40 . However, diffusion-based approaches lack explicit mechanisms for temporal evolution, making long-horizon prediction and causal consistency difficult to maintain 41 . Latent diffusion formulations further compress physical states into low-dimensional representations 42,43 , reducing interpretability and potentially obscuring underlying physics. In addition, iterative denoising procedures remain computationally demanding, limiting their suitability for real-time or long-duration simulations.
These developments expose a fundamental tension in data-driven modelling of multiscale dynamical systems: models optimised for stable long-term temporal evolution typically operate at coarse resolution and struggle to recover fine-scale structure, while models capable of high-resolution spatial reconstru
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