Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correction

Diffusion models (DMs) have demonstrated remarkable success in real-world image super-resolution (SR), yet their reliance on time-consuming multi-step sampling largely hinders their practical applications. While recent efforts have introduced few- or single-step solutions, existing methods either inefficiently model the process from noisy input or fail to fully exploit iterative generative priors, compromising the fidelity and quality of the reconstructed images. To address this issue, we propose FlowSR, a novel approach that reformulates the SR problem as a rectified flow from low-resolution (LR) to high-resolution (HR) images. Our method leverages an improved consistency learning strategy to enable high-quality SR in a single step. Specifically, we refine the original consistency distillation process by incorporating HR regularization, ensuring that the learned SR flow not only enforces self-consistency but also converges precisely to the ground-truth HR target. Furthermore, we introduce a fast-slow scheduling strategy, where adjacent timesteps for consistency learning are sampled from two distinct schedulers: a fast scheduler with fewer timesteps to improve efficiency, and a slow scheduler with more timesteps to capture fine-grained texture details. Extensive experiments demonstrate that FlowSR achieves outstanding performance in both efficiency and image quality. Code: this https URL.

The effectiveness of super resolution (SR) models hinges on their ability to recover high frequency structure without introducing artifacts. Diffusion based approaches have recently advanced the state of the art in SR. However, most diffusion based SR pipelines operate purely in the spatial domain, which may yield high frequency details that are not well supported by the underlying low resolution evidence. On the other hand, unlike supervised SR models that may inject dataset specific textures, single image SR relies primarily on internal image statistics and can therefore be less prone to dataset-driven hallucinations; nevertheless, ambiguity in the LR observation can still lead to inconsistent high frequency details. To tackle this problem, we introduce BATDiff, an unsupervised Bivariate A trous Wavelet Diffusion model designed to provide structured cross scale guidance during the generative process. BATDiff employs an a Trous wavelet transform that constructs an undecimated multiscale representation in which high frequency components are progressively revealed while the full spatial resolution is preserved. As the core inference mechanism, BATDiff includes a bivariate cross scale module that models parent child dependencies between adjacent scales. It improves high frequency coherence and reduces mismatch artifacts in diffusion based SR. Experiments on standard benchmarks demonstrate that BATDiff produces sharper and more structurally consistent reconstructions than existing diffusion and non diffusion baselines, achieving improvements in fidelity and perceptual quality.

Most super-resolution models learn from paired data by supervising only the final high-resolution output. This provides little control over how the prediction should evolve between the downsampled observation and its fine target. We introduce GalerkinFlow, an equation-agnostic framework that turns each coarse--fine pair into supervision along an entire reconstruction path. At a random sample of intermediate states on the reconstruction path, the model predicts the coarse-to-fine residual velocity and uses coarse-anchor point to define a pseudo-endpoint. We show that the reconstruction loss of this pseudo-endpoint is exactly related to the intermediate velocity loss through a known time-dependent weight. Consequently, every intermediate state contributes supervision toward the same fine target, rather than serving only as an internal step toward an endpoint loss. Because intermediate states already reveal part of the missing fine-scale structure, we additionally supervise the coarse endpoint used during one-step inference. A finite-difference objective further constrains local spatial variation. GalerkinFlow combines convolutional features with scale-conditioned Galerkin operator mixing and requires no governing equation or physical metadata. It achieves the lowest raw-space errors among the evaluated equation-agnostic baselines on Navier--Stokes and Darcy Flow, while remaining competitive on DIV2K.