Arbitrary-Scale Super-Resolution (ASR) reconstructs images at continuous magnification factors. Recent methods accelerate inference by replacing computationally heavy implicit neural decoders with explicit 2D Gaussian Splatting (GS). However, since standard Gaussians are smooth low-pass primitives, modeling edges and fine textures requires multiple overlapping, well-aligned splats, which creates severe bottlenecks during rasterization. To address this, we introduce Resonant Brane Splatting (RBS), a feed-forward ASR framework. RBS replaces flat Gaussians with Branes: expressive primitives that emit spatially varying colors to natively model local contrast and complex textures within a single footprint. We achieve this by augmenting the standard Gaussian envelope with internal Gaussian-Hermite modes, assigning a distinct color coefficient to each. The zero-order mode recovers standard GS, while higher-order modes capture high frequencies. We predict Brane parameters directly from low-resolution features. Because Branes provide a mathematically richer formulation than simple Gaussians, far fewer primitives need to overlap to reconstruct a given target pixel. To exploit this, we introduce an efficient fully differentiable rasterizer with a precise culling strategy based on the classical quantum turning point. This allows us to safely skip negligible regions, drastically reducing the rendering overhead. Experiments on standard ASR benchmarks show that RBS improves reconstruction quality over implicit and GS baselines, while achieving superior speed-quality trade-off than prior GS methods.

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