# CubicSplat: Differentiable Vector Graphics via Error-Bounded Forward Relaxation

arXiv: https://arxiv.org/abs/2608.20803 · HTML: https://mlsanity.com/paper/2608.20803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 30 of 30)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [StopThePop: Sorted Gaussian Splatting for View-Consistent Real-time Rendering](https://mlsanity.com/paper/2402.00525/) (2024)
- [Im2Vec: Synthesizing Vector Graphics without Vector Supervision](https://mlsanity.com/paper/2102.02798/) (2021)
- [VectorFusion: Text-to-SVG by Abstracting Pixel-Based Diffusion Models](https://mlsanity.com/paper/2211.11319/) (2022)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [Towards Layer-wise Image Vectorization](https://mlsanity.com/paper/2206.04655/) (2022)
- [SVGDreamer: Text Guided SVG Generation with Diffusion Model](https://mlsanity.com/paper/2312.16476/) (2023)
- [A Compact Dynamic 3D Gaussian Representation for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2311.12897/) (2023)
- [DiffSketcher: Text Guided Vector Sketch Synthesis through Latent Diffusion Models](https://mlsanity.com/paper/2306.14685/) (2023)
- [Approximate Differentiable Rendering with Algebraic Surfaces](https://mlsanity.com/paper/2207.10606/) (2022)
- [B'ezierSketch: A generative model for scalable vector sketches](https://mlsanity.com/paper/2007.02190/) (2020)
- [Image-GS: Content-Adaptive Image Representation via 2D Gaussians](https://mlsanity.com/paper/2407.01866/) (2024)
- [4D LangSplat: 4D Language Gaussian Splatting via Multimodal Large Language Models](https://mlsanity.com/paper/2503.10437/) (2025)
- [Text-to-Vector Generation with Neural Path Representation](https://mlsanity.com/paper/2405.10317/) (2024)
- [TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes](https://mlsanity.com/paper/2405.20283/) (2024)
- [SuperSVG: Superpixel-based Scalable Vector Graphics Synthesis](https://mlsanity.com/paper/2406.09794/) (2024)
- [Does 3D Gaussian Splatting Need Accurate Volumetric Rendering?](https://mlsanity.com/paper/2502.19318/) (2025)
- [Layered Image Vectorization via Semantic Simplification](https://mlsanity.com/paper/2406.05404/) (2024)
- [Segmentation-guided Layer-wise Image Vectorization with Gradient Fills](https://mlsanity.com/paper/2408.15741/) (2024)
- [A Simple Approach to Differentiable Rendering of SDFs](https://mlsanity.com/paper/2405.08733/) (2024)
- [Bezier Splatting for Fast and Differentiable Vector Graphics Rendering](https://mlsanity.com/paper/2503.16424/) (2025)
- [Image Vectorization with Depth: convexified shape layers with depth ordering](https://mlsanity.com/paper/2409.06648/) (2024)

## Abstract (arXiv)

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 B'ezier closest-point solvers with uniform polyline surrogates whose geometric error is bounded at 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 4x faster than prior methods. The code is available at https://github.com/CubicSplat/repo