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name: score_sde_kernels description: Define Score SDE VE, VP, and sub-VP kernels with reverse and probability-flow drift checks.

Score SDE Kernels

Use this skill when you need the forward perturbation kernels from "Score-Based Generative Modeling through Stochastic Differential Equations" or when a recovery experiment needs reverse-time SDE or probability-flow drift algebra without the original repository.

Do not use this skill as a replacement for a trained score network, FID evaluation, or a full image-generation pipeline. It supplies the deterministic SDE math that other skills can consume.

Inputs

• family: one of ve, vp, or subvp.
• Schedule parameters: sigma_min and sigma_max for VE; beta_min and beta_max for VP and sub-VP.
• State values as scalars or lists of floats.
• Time t in [0, 1].
• Optional score callback score_fn(x, t) for reverse-time or probability-flow drifts.

Outputs

• Forward drift and diffusion.
• Gaussian marginal mean and standard deviation.
• Prior samples and prior log densities.
• Reverse-time SDE drift f - g^2 score.
• Probability-flow ODE drift f - 0.5 g^2 score.

Workflow

1. Instantiate SDEKernel from scripts/sde_kernels.py with the required family and schedule.
2. Use sde(x, t) for forward drift and diffusion.
3. Use marginal_prob(x0, t) to perturb data and construct score-matching targets.
4. Use reverse_drift(x, t, score_fn, probability_flow=False) for reverse SDE drift.
5. Use reverse_drift(..., probability_flow=True) for the probability-flow ODE drift.
6. Save numerical checks in recovery logs when accepting a proxy experiment.

Validation

Run:

python scripts/sde_kernels.py --self-test
python tests/test_sde_kernels.py

The tests verify VP/sub-VP marginal bounds, VE prior log probability, and the half-correction identity for probability flow.

Limitations

This skill intentionally uses standard-library math and one-dimensional or vector fixtures. It preserves the paper's SDE contracts, but it does not implement neural architectures, dataset pipelines, or high-resolution image sampling.