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name: score_sde_probability_flow description: Compute Score SDE probability-flow drift identities and compact likelihood accounting diagnostics.

Score SDE Probability Flow

Use this skill when you need deterministic probability-flow ODE drift checks or lightweight likelihood accounting for Score SDE recovery. It is designed for scalar or low-dimensional fixtures and can cross-check the SDE kernel skill.

Do not use this skill to claim the paper's CIFAR-10 bits/dim unless it is connected to a trained model, data preprocessing, ODE solver, and evaluation pipeline that match the paper.

Inputs

• Forward drift f(x, t).
• Diffusion g(t).
• Score function.
• Prior log probability at terminal latent.
• Divergence values or a finite-difference divergence callback.
• Data dimension and optional offset for bits/dim.

Outputs

• Probability-flow drift.
• Divergence estimate.
• Delta log probability.
• Negative log likelihood or bits/dim proxy.
• Identity checks comparing reverse SDE and probability-flow drifts.

Workflow

1. Compute probability-flow drift as f - 0.5 * g^2 * score.
2. Estimate divergence analytically or with finite differences.
3. Accumulate a pathwise delta logp term with the chosen integration direction.
4. Combine terminal prior logp and delta logp.
5. Convert to bits/dim only when the dimensionality and offset are explicitly supplied.

Validation

Run:

python scripts/probability_flow.py --self-test
python tests/test_probability_flow.py

The tests verify half-correction drift, finite-difference divergence on a linear function, and scalar likelihood accounting.

Limitations

This skill handles mechanism-faithful diagnostics, not black-box adaptive ODE integration over image batches.