Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows

TL;DR

Multiscale spatiotemporal flows pose a challenge for long-horizon accuracy and fine-scale fidelity. Uni-Flow decouples temporal evolution from spatial refinement into a low-resolution autoregressive core and a diffusion-based upscaling operator, enabling stable long-term predictions and high-resolution detail. The approach is validated on 2D Kolmogorov flow, 3D turbulent channel inflow generation with a quantum-informed prior, and patient-specific stenotic aortic flow, achieving faster-than-real-time inference and faithful statistics across scales. This framework provides a general, architecture-agnostic pathway toward real-time, physics-consistent surrogates for complex flows, with potential synergy with quantum machine learning.

Abstract

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.

Figures (5)

• Figure 1: Uni-Flow framework for multiscale spatiotemporal modelling and representative applications. Uni-Flow decouples temporal evolution and spatial refinement through a unified autoregressive–diffusion formulation. High-resolution physical fields are first downsampled to a low-resolution representation, that retains the large-scale degrees of freedom governing long-horizon temporal evolution relevant to the target observables. The AR component may be instantiated using different operator-learning architectures, such as neural operators or Koopman-based models, to ensure stable long-horizon temporal dynamics. At selected timesteps, the low-resolution state is upscaled and provided as conditioning to a diffusion-based refinement model, which reconstructs high-resolution physical fields and recovers fine-scale spatial structure through a small number of denoising steps. The lower panels illustrate representative applications of Uni-Flow across increasing physical and modelling complexity: two-dimensional Kolmogorov flow ($256 \times 256$), three-dimensional turbulent channel inflow generation ($192 \times 192$), and patient-specific stenotic aortic flow, where surface pressure fields are parameterised on a two-dimensional UV domain ($512 \times 512$).
• Figure 2: Evaluation of the Uni-Flow model on the two-dimensional Kolmogorov flow. Panel (a) shows sequential vorticity snapshots for the ground truth (top), low-resolution autoregressive (LR-AR) prediction (middle), and absolute error (bottom), where LR-AR captures the dominant shear-layer dynamics but under-resolves fine-scale vortices. Panel (b) presents the time-averaged vorticity field, showing that the LR-AR model reproduces the large-scale roll structures imposed by the Kolmogorov forcing. Panel (c) displays the temporal autocorrelation, indicating stable short-term dynamics with gradual decay at longer horizons. Panel (d) shows the time-averaged kinetic energy spectrum $\langle E(k) \rangle$, demonstrating consistent inertial scaling but slight underestimation at high wavenumbers. Panel (e) presents the Q-Q comparison between predicted and ground-truth vorticity distributions, confirming statistical alignment with minor deviation in the tails.
• Figure 3: Demonstration of Uni-Flow for generating turbulent inflow conditions in a channel-flow configuration. Panel (a) presents the time-averaged velocity comparison between Reference, LR-AR, and Uni-Flow over 600 time frames. Panel (b) shows instantaneous streamwise velocity fields for the reference LBM-LES (left), LR-AR baseline (middle), and Uni-Flow prediction (right). Panel (c) displays the streamwise energy spectrum, confirming that Uni-Flow recovers both the inertial and dissipative ranges with higher fidelity than LR-AR. The blue, red and green lines are representing reference data, Uni-Flow, and LR-AR cases respectfully. Panel (d) shows the time-averaged normalised turbulence velocity profiles, where Uni-Flow matches the reference at all scales, whereas, LR-AR failed to match near the wall. Panel (e) presents the probability density function of normalised velocity distribution, demonstrating that Uni-Flow reproduces the correct velocity distribution whereas LR-AR case failed to capture the low velocity region.
• Figure 4: Uni-Flow learning of spatiotemporal pressure dynamics in aortic stenosis. Panel (a) Overview of the Uni-Flow framework for complex cardiovascular flows. Three-dimensional numerical simulations (HemeLB) of a stenotic aorta are mapped to a two-dimensional UV domain, where Uni-Flow learns the spatiotemporal evolution of wall pressure fields entirely in 2D. The predicted fields are then inversely mapped to the three-dimensional geometry to reconstruct the physical distribution on the aortic surface. Panel (b) Comparison of wall pressure evolution across a cardiac cycle at 5 representative time frames ($t_1$ to $t_5$). Uni-Flow accurately reproduces the high-pressure buildup upstream of the stenosis and the downstream recovery region, closely matching the ground-truth simulation results both spatially and temporally.
• Figure 5: Quantitative assessment of pressure dynamics in stenotic aortic flow. Panel (a) shows the ensamble average surface pressure distributions on the aortic wall for the ground truth (left), LR-AR (middle), and Uni-Flow (right), where Uni-Flow accurately captures the high-pressure region upstream of the stenosis and the recovery downstream. Panel (b) presents the temporal autocorrelation functions, showing that Uni-Flow maintains periodic coherence across cardiac cycles. Panel (c) displays the pressure kernel density estimate plots, indicating that Uni-Flow reproduces the sharp, narrow distribution observed in the HemeLB reference. Panel (d) shows the pressure energy spectra for the peak of heart beat cycle, demonstrating that Uni-Flow recovers the correct spectral scaling and dissipation range across all resolved wavenumbers, while LR-AR model failed to capture the high wave number energy spectrum. Panel (e) quantifies the pressure-drop characteristics within the highlighted region over 8 cardiac cycles (200 inference frames), comparing peak amplitudes, statistical distributions, and temporal waveforms. Uni-Flow remains within the simulated physiological range of 90-115 mmHg, accurately reproducing pulsatile amplitude and phase while matching the mean and variability of the reference. In contrast, the LR-AR baseline underestimates systolic peaks and shows reduced dynamic range.