Thera: Aliasing-Free Arbitrary-Scale Super-Resolution with Neural Heat Fields

TL;DR

Thera tackles aliasing in arbitrary-scale SR by modeling the image with neural heat fields that solve the isotropic heat equation $\partial \Phi/\partial t = \kappa \nabla_{\mathbf{x}}^2 \Phi$, embedding a Gaussian PSF whose blur is controlled by a time input $t$ to enable analytically exact anti-aliasing at any target scale. The method learns a multi-scale prior via a hypernetwork that conditions local neural heat fields on a shared frequency bank $\mathbf{W}_1$, producing an end-to-end SR system that is parameter-efficient. A total-variation regularizer on $\Phi(\mathbf{x},0)$ improves generalization to out-of-distribution scales, and extensive experiments show Thera outperforming prior ASR methods in PSNR on DIV2K and standard benchmarks while maintaining lower parameter overhead. The work provides theoretical and practical guarantees for multi-scale representation and anti-aliasing in neural-field-based SR, and suggests broader potential for physics-informed implicit representations in vision tasks.

Abstract

Recent approaches to arbitrary-scale single image super-resolution (ASR) use neural fields to represent continuous signals that can be sampled at arbitrary resolutions. However, point-wise queries of neural fields do not naturally match the point spread function (PSF) of pixels, which may cause aliasing in the super-resolved image. Existing methods attempt to mitigate this by approximating an integral version of the field at each scaling factor, compromising both fidelity and generalization. In this work, we introduce neural heat fields, a novel neural field formulation that inherently models a physically exact PSF. Our formulation enables analytically correct anti-aliasing at any desired output resolution, and -- unlike supersampling -- at no additional cost. Building on this foundation, we propose Thera, an end-to-end ASR method that substantially outperforms existing approaches, while being more parameter-efficient and offering strong theoretical guarantees. The project page is at https://therasr.github.io.

Figures (11)

• Figure 1: We present Thera, the first method for arbitrary-scale super-resolution with a built-in physical observation model. Given an input image, a hypernetwork predicts the parameters of a specially designed neural heat field, inherently decomposing the image into sinusoidal components. The field's architecture automatically attenuates frequencies as a function of the scaling factor so as to match the output resolution at which the signal is re-sampled.
• Figure 2: Comparison of recent ASR methods, averaged over $\times\{2,3,4\}$ scales. We generally achieve higher performance at lower parameter counts. Our best model, Thera Pro, achieves highest overall performance by a large margin.
• Figure 3: Overview of Thera. A hypernetwork estimates parameters $\{\bm{b}_1, \bm{W}_2\}^{(i,j)}$ of pixel-wise, local neural heat fields. The phase shifts $\bm{b}_1$ operate on globally learned components, before thermal activations scale each component depending on their frequency and the desired scaling factor. The components are then linearly combined using coefficients $\bm{W}_2$, resulting in an appropriately-blurred, continuous local neural field. This field is then rasterized at the appropriate sampling rate (resolution) to yield a part of the final output image (red square).
• Figure 4: Qualitative examples for a representative $\times$6 scale factor, with an RDN zhang2018residual backbone for all methods. Best viewed zoomed in.
• Figure 5: Thera reconstructs a signal $\Phi$ and its gradient $\nabla_{\mathbf{x}}\Phi$ more faithfully than a ReLU-based competitor chen2021learning. Due to its natural, Fourier-inspired representation, Thera is also infinitely differentiable, while ReLU-based competitors approximate the signal as a piecewise-linear function with null higher derivatives (last row).