Generative Learning for Turbulence: Conditional Diffusion and Flow Matching Models for Spatiotemporal Flow Synthesis and Reconstruction

This talk presents our recent advances in generative modeling of wall-bounded turbulence using conditional diffusion and flow matching. We introduce a unified generative learning framework that integrates latent diffusion processes, neural field conditioning, and stochastic transport to enable high-fidelity synthesis and reconstruction of instantaneous spatiotemporal turbulent flows given various conditions.

The Conditional Neural Field Latent Diffusion (CoNFiLD) model generates full-field spatiotemporal velocity realizations conditioned on sparse measurements, low-resolution observations, or initial/boundary data. Its inflow extension, CoNFiLD-inlet, enables the synthesis of spatially and temporally coherent turbulence across a range of Reynolds numbers, providing robust inflow conditions for DNS and LES. A Bayesian extension introduces uncertainty quantification via sampling from the conditional posterior distribution over turbulent fields.

To complement these capabilities, we developed a conditional flow matching framework that learns a continuous-time transport map for posterior-consistent generation of near-wall turbulence from wall-based measurements. Coupled with a SWAG-trained forward operator, this likelihood-free approach enables zero-shot generalization and uncertainty-aware reconstruction without adversarial training or score matching.

Together, these models establish a generative paradigm for turbulence modeling—probabilistic, physics-informed, and computationally scalable. By integrating deep generative learning with differentiable solvers and structured conditioning, this framework supports a wide range of tasks, including inflow generation, wall modeling, and data assimilation. The talk will highlight key concepts, algorithms, and results from our recent work, offering a broadly accessible perspective for the fluid dynamics community.