CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation

Vector graphics are prized for their resolution independence,compact storage, and direct editability, making differentiable optimiza-tion of their parametric primitives an attractive goal. Yet classical ras-terization is discontinuous with respect to geometry, and existing reme-dies that smooth the forward pass demand increasingly elaborate heuris-tics as scene complexity grows. We trace this fragility to a gradientseesaw: design choices that improve forward geometric exactness cansystematically degrade the induced gradient signal, and vice versa. Tonavigate this tension we introduce CubicSplat, a differentiable vectorrasterizer that replaces Bézier closest-point solvers with uniform poly-line surrogates whose geometric error is bounded at O(S −2 ). The re-sulting static computation graph yields well-conditioned gradients byconstruction, while a compositing-derived visibility mechanism prunesdegenerate primitives without auxiliary regularization. On DIV2K andKodak benchmarks CubicSplat achieves state-of-the-art reconstructionquality with over 2 dB PSNR gain in the closed-fill setting, while train-ing up to 4× faster than prior methods. The code is available at https://github.com/CubicSplat/repo