<p>We present Neural Diffusion Curves (NDC), a differentiable framework that vectorizes raster images into compact, editable diffusion curve representations in a single forward pass. Unlike traditional multi-stage pipelines that rely on handcrafted feature extraction and non-differentiable numerical solvers, NDC unifies curve geometry prediction, bilateral color control point extraction, and PDE-based rendering within a learnable architecture. Specifically, a Transformer-based curve decoder with optimal transport matching produces a data-adaptive set of sparse Bézier curves; a lightweight 1D convolutional network extracts color constraints along curve normals; and a Fourier Neural Operator (FNO) serves as a differentiable surrogate for the Poisson solver, enabling gradient propagation across the entire pipeline. On <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$512 \times 512$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>512</mn> <mo>×</mo> <mn>512</mn> </mrow> </math></EquationSource> </InlineEquation> flat illustrations, NDC achieves about <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$18\times $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>18</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation> pipeline-level speedup over the fastest classical diffusion curve baseline and a nearly <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$900\times $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>900</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation> speedup over the slowest, while reducing the curve count by over <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$75\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>75</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> and producing significantly longer, semantically coherent curves. NDC attains competitive perceptual fidelity (LPIPS) at the cost of a moderate increase in pixel-level error (RMSE), a trade-off that favors applications where speed, compactness, and direct editability are of primary importance.</p>

NDC: Neural Diffusion Curves for image vectorization

期刊论文
发表日期：

2026年7月20日

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Yifan Huang,
Wuyu Yang,
Hao Xie,
Yu-Kun Lai,
Yao Jin,
Huaxiong Zhang,
Lili He

摘要

We present Neural Diffusion Curves (NDC), a differentiable framework that vectorizes raster images into compact, editable diffusion curve representations in a single forward pass. Unlike traditional multi-stage pipelines that rely on handcrafted feature extraction and non-differentiable numerical solvers, NDC unifies curve geometry prediction, bilateral color control point extraction, and PDE-based rendering within a learnable architecture. Specifically, a Transformer-based curve decoder with optimal transport matching produces a data-adaptive set of sparse Bézier curves; a lightweight 1D convolutional network extracts color constraints along curve normals; and a Fourier Neural Operator (FNO) serves as a differentiable surrogate for the Poisson solver, enabling gradient propagation across the entire pipeline. On $512 \times 512$ $512 \times 512$ flat illustrations, NDC achieves about $18\times $ $18 \times$ pipeline-level speedup over the fastest classical diffusion curve baseline and a nearly $900\times $ $900 \times$ speedup over the slowest, while reducing the curve count by over $75\%$ $75 %$ and producing significantly longer, semantically coherent curves. NDC attains competitive perceptual fidelity (LPIPS) at the cost of a moderate increase in pixel-level error (RMSE), a trade-off that favors applications where speed, compactness, and direct editability are of primary importance.