# Multiscale Hypersonic Boundary Layer Reconstruction via Spectral Binning and Subdomain-wise Conditional Diffusion

arXiv: https://arxiv.org/abs/2606.15023 · HTML: https://mlsanity.com/paper/2606.15023/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 15 of 15)

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- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [SyncDiffusion: Coherent Montage via Synchronized Joint Diffusions](https://mlsanity.com/paper/2306.05178/) (2023)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Mixture of Diffusers for scene composition and high resolution image generation](https://mlsanity.com/paper/2302.02412/) (2023)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [3D MedDiffusion: A 3D Medical Latent Diffusion Model for Controllable and High-quality Medical Image Generation](https://mlsanity.com/paper/2412.13059/) (2024)
- [Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation](https://mlsanity.com/paper/2311.07896/) (2023)
- [Binned Spectral Power Loss for Improved Prediction of Chaotic Systems](https://mlsanity.com/paper/2502.00472/) (2025)
- [MedDiff-FM: A Diffusion-based Foundation Model for Versatile Medical Image Applications](https://mlsanity.com/paper/2410.15432/) (2024)

## Abstract (arXiv)

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.