NDC: Neural Diffusion Curves for image vectorization

doi:10.1007/s00371-026-04594-9

NDC: Neural Diffusion Curves for image vectorization

2026-07-20

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DOI：10.1007/s00371-026-04594-9

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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 $$512 \times 512$$ flat illustrations, NDC achieves about $$18\times $$ pipeline-level speedup over the fastest classical diffusion curve baseline and a nearly $$900\times $$ speedup over the slowest, while reducing the curve count by over $$75\%$$ 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.

Keywords:

Diffusion curves

Image vectorization

Differentiable curve extraction

Differentiable rendering

Fourier neural operator

NDC: Neural Diffusion Curves for image vectorization

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