---

name: score_sde_probability_flow description: Build deterministic probability-flow ODE diagnostics and one-dimensional likelihood corrections for Score SDE recovery.

Score SDE Probability Flow

Use this skill when a recovery experiment must show the deterministic ODE counterpart of the reverse SDE or a likelihood-style divergence check.

Inputs

• State value.
• Time value.
• Forward drift and diffusion or simple VP-like coefficients.
• Score and score derivative for exact low-dimensional tests.

Outputs

• ODE drift.
• Zero diffusion flag.
• Divergence and log-density correction.
• Finite-step diagnostic.

Workflow

1. Compute probability-flow drift with half the reverse-SDE score correction.
2. Set diffusion to zero.
3. Compute exact one-dimensional divergence when using a linear score.
4. Apply one Euler step and accumulate the negative divergence as a log-density correction.
5. Record that this is a proxy diagnostic unless full image scaling is provided.

Validation

Run:

python tests/test_probability_flow.py
python scripts/probability_flow.py --x 1.0 --t 0.5 --score-coeff -1.0

Limitations

This skill validates probability-flow mechanics; it does not report CIFAR-10 bits/dim without the full trained model and data pipeline.