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Kernel-Gradient Drifting Models

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion theory and learned samplers · 0 citations (OpenAlex)

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Proposes kernel-gradient drifting, which replaces the Euclidean displacement in drifting models with the kernel's own gradient, giving a score-ratio interpretation, identifiability for characteristic kernels, and extensions to Riemannian manifolds and discrete data via the Fisher-Rao simplex.

Problem

Drifting models for one-step generation are theoretically understood only for Gaussian kernels; with general (e.g., Laplace) kernels the Euclidean displacement direction breaks identifiability and the method is unclear on non-Euclidean domains.

Approach

Define the drift as the difference of normalized kernel gradients (not kernel-weighted displacements), which equals the difference of log kernel-smoothed densities, so the drift is a smoothed score ratio; this yields identifiability for characteristic kernels and transfers intrinsically to manifolds via Riemannian gradients and Exp maps.

Key results

• On the Earth benchmark, spherical Gaussian gradient drifting achieves the best MMD on Volcano (0.112 vs 0.146 for the Euclidean Laplace drifting baseline).
• On QM9, spherical Laplace gradient drifting reaches 38.9% validity and 44.1% uniqueness versus 22.0% and 40.0% for Euclidean Laplace drifting.
• On promoter DNA, spherical Gaussian gradient drifting reaches 0.90 6-mer correlation, slightly above the best flow-distilled baseline E-RMF + v-pred at 0.96 being higher, i.e. it narrows but does not close the gap.

Surprising findings

• The Spherical Gaussian Gradient variant is much worse on Earthquake (MMD 0.158) than the Euclidean Laplace baseline, indicating instability across datasets.
• On QM9, the teacher-free spherical gradient drifting matches PairFlow (+DCD) uniqueness (44.1%) while exceeding it on validity-related comparisons only partially; validity is 38.9% vs 44.3%.

Limitations

• Results are sensitive to hyperparameter choice, according to the authors.
• Only Matérn kernels are studied, not a broader kernel class.
• Training stability is not analyzed; the smoothed-KL result holds only in Euclidean space per the appendix.

Experimental setup

Datasets: checkerboard (synthetic) swissroll (synthetic) Earth events benchmark (Volcano, Earthquake, Fire, Flood) promoter DNA QM9

Benchmarks: Earth events benchmark (MMD) QM9 validity and uniqueness promoter DNA 6-mer correlation synthetic checkerboard and swissroll SW-2 and tile accuracy Matérn swissroll C2ST

Metrics: MMD sliced Wasserstein-2 tile accuracy C2ST geodesic Sinkhorn 1-NN accuracy 6-mer correlation validity uniqueness

Baselines: Euclidean Laplace drifting E-RMF S-RMF L-RMF UDLM PairFlow ReDi

Builds on: drifting models score matching Matérn kernels on manifolds Fisher-Rao geometry of the simplex

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