CubicSplat: Differentiable Vector Graphics via
Error-Bounded Forward Relaxation

Chenglong Liu¹ Xin Zhang¹ Yimeng Zhu¹ Liyang He¹ Yixiao Ma¹ Yu Su^2,3 Zhenya Huang¹ Qi Liu^1,✉

¹ State Key Laboratory of Cognitive Intelligence, University of Science and Technology of China, Hefei, China

² Hefei Normal University, Hefei, China

³ Zhejiang Key Laboratory of Intelligent Education Technology and Application, Zhejiang Normal University, Jinhua, China

ECCV 2026 Oral

Qualitative CubicSplat results across varying curve budgets, topology modes, and datasets, from low-budget stylization to a high-budget reconstruction of a half-timbered façade. — Qualitative results across varying budgets, topology modes, and datasets. At low budgets (closed 128, open/closed 256), CubicSplat preserves clean boundaries and smooth color gradients, producing coherent stylization rather than noisy artifacts. At higher budgets (open 1024, closed 2048), fine details such as the half-timbered façade emerge faithfully, confirming that the gradient oracle scales from compact stylization to high-fidelity reconstruction.

Abstract

Vector graphics are prized for their resolution independence, compact storage, and direct editability, making differentiable optimization of their parametric primitives an attractive goal. Yet classical rasterization is discontinuous with respect to geometry, and existing remedies that smooth the forward pass demand increasingly elaborate heuristics as scene complexity grows. We trace this fragility to a gradient seesaw: design choices that improve forward geometric exactness can systematically degrade the induced gradient signal, and vice versa. To navigate this tension we introduce CubicSplat, a differentiable vector rasterizer that replaces Bézier closest-point solvers with uniform polyline surrogates whose geometric error is bounded at \(\mathcal{O}(S^{-2})\). The resulting static computation graph yields well-conditioned gradients by construction, while a compositing-derived visibility mechanism prunes degenerate primitives without auxiliary regularization. On DIV2K and Kodak benchmarks CubicSplat achieves state-of-the-art reconstruction quality with over 2 dB PSNR gain in the closed-fill setting, while training up to 4\(\times\) faster than prior methods.

Keywords: Differentiable rendering · Vector graphics · Scene representation · Gradient conditioning

Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (62525606, U25B2072) and Open Research Fund of Zhejiang Key Laboratory of Intelligent Education Technology and Application (No. 2025ZNJYKF006).