Generative Super-Resolution

Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy. We apply four generative diffusion modeling approaches to super-resolution and inference of forced two-dimensional quasi-geostrophic turbulence on the beta-plane from coarse, sparse, and gappy observations. Two guided approaches minimally adapt a pre-trained unconditional model: SDEdit modifies the initial condition, and Diffusion Posterior Sampling (DPS) modifies the reverse diffusion process score. Two conditional approaches, a vanilla variant and classifier-free guidance, require training with paired high-resolution and observation data. We consider multiple test cases spanning: two regimes, eddy and anisotropic-jet turbulence; two Reynolds numbers, 10^3 and 10^4; and two observation types, 4x coarse-resolution fields and coarse, sparse and gappy observations. Our comprehensive skill metrics include norms of the reconstructed vorticity fields, turbulence statistical quantities, and quantifications of the super-resolved probabilistic ensembles and their errors. We also study the sensitivity to tuning parameters such as guidance strength. Results show that the generated super-resolution fields of SDEdit are unphysical, while those of DPS are reasonable but with smoothed fine-scale features; however, neither of these lower-cost models propagates observational information effectively to unobserved regions. The two conditional models require re-training, but reconstruct missing fine-scale features, are cycle-consistent with observations, and predict correct turbulence statistics, including the tails. Further, their mean errors are highly correlated with and predictable from their ensemble standard deviations. Results highlight the tradeoffs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment.

Burst image super-resolution (BISR) reconstructs a high-resolution keyframe by aggregating complementary sub-pixel evidence from a short burst of low-resolution frames. Existing methods often process all burst frames with heavy backbones or maintain deep cross-frame interaction throughout the network, leading to redundant computation on non-key frames and limiting scalability with burst length. In this work we propose BurstMamba, a BISR architecture built on a simple principle: allocate most compute to reconstructing the keyframe, and process the burst primarily to extract sub-pixel priors. To this end, BurstMamba decouples BISR into a high-capacity keyframe super-resolution stream and a lightweight burst stream that interacts with it only through stage-wise residual injection. To improve burst-to-keyframe transfer, we introduce Gather -> Aggregate -> Scatter (GAS), which uses correspondence only for cross-frame message passing while preserving native-view features through a residual connection, and a wavelet-conditioned state update that biases selective routing toward high-frequency regions. Across SyntheticSR, RealBSR-RAW, and RealBSR-RGB, BurstMamba achieves state-of-the-art results. Extensive ablations show that the proposed compute separation, GAS, and wavelet-conditioned routing each contribute to the model's accuracy and scaling.

Hyperspectral imaging is a powerful bioimaging tool which can uncover novel insights, thanks to its sensitivity to the intrinsic properties of materials. However, this enhanced contrast comes at the cost of system complexity, constrained by an inherent trade-off between spatial, spectral, and temporal resolution. To overcome this limitation, we present a self-supervised deep learning-based approach that restores and enhances pixel resolution post-acquisition without requiring external training data beyond the images to be restored. Fine-tuned using metrics aligned with the imaging model, our physics-aware method achieves a 16$\times$ pixel super-resolution enhancement and a 12$\times$ imaging speedup without the need of additional training data for transfer learning. Applied to both synthetic and experimental data from five different sample types, including healthy and diseased tissues, we demonstrate that the model preserves biological integrity, as we did not detect systematic loss of biological features or biologically consequential hallucinations in tested datasets. We also concretely demonstrate the model's ability to reveal disease-associated metabolic changes that would otherwise remain undetectable. Furthermore, we provide physical insights into the model's inner workings, paving the way for future refinements that could potentially reveal novel high resolution features in an explainable manner. All methods are available as open-source software on GitHub.

Autoencoders have found widespread application in both their original deterministic form and in their variational formulation (VAEs). In scientific applications and in image processing it is often of interest to consider data that are viewed as functions; while discretisation (of differential equations arising in the sciences) or pixellation (of images) renders problems finite dimensional in practice, conceiving first of algorithms that operate on functions, and only then discretising or pixellating, leads to better algorithms that smoothly operate between resolutions. In this paper function-space versions of the autoencoder (FAE) and variational autoencoder (FVAE) are introduced, analysed, and deployed. Well-definedness of the objective governing VAEs is a subtle issue, particularly in function space, limiting applicability. For the FVAE objective to be well defined requires compatibility of the data distribution with the chosen generative model; this can be achieved, for example, when the data arise from a stochastic differential equation, but is generally restrictive. The FAE objective, on the other hand, is well defined in many situations where FVAE fails to be. Pairing the FVAE and FAE objectives with neural operator architectures that can be evaluated on any mesh enables new applications of autoencoders to inpainting, superresolution, and generative modelling of scientific data.

Single image super-resolution aims to reconstruct high-resolution images from low-resolution inputs. This paper proposes FreeTransformSR, a novel lightweight super-resolution network based on a channel-wise free low-rank learnable transform. The transform learns task-adaptive basis functions in a data-driven manner, enabling adaptive feature modulation with minimal parameter overhead. To further enhance high-frequency detail recovery, we introduce a local feature modulation branch that complements transform-domain processing with depthwise convolution. In addition, a soft complexity adaptive module dynamically fuses the outputs of local convolution and window self-attention branches through a lightweight gating network, adaptively adjusting the fusion ratio based on regional texture characteristics. An adaptive intensity modulation strategy is also incorporated to adjust transform-domain response strength at the sample level, enabling the network to dynamically adjust processing intensity according to input features. Extensive experiments on five benchmark datasets demonstrate that FreeTransformSR achieves competitive PSNR/SSIM performance with significantly fewer parameters and FLOPs. Specifically, FreeTransformSR achieves 32.41 dB on BSD100 x2 and 27.00 dB on Urban100 x4 with only 595K parameters, while delivering faster inference speed than competing methods, making it well-suited for deployment in resource-constrained scenarios. Source code is available at: https://github.com/HJiLi/FreeTransformSR.