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name: conditional_ot_paths description: Construct and validate Flow Matching conditional optimal-transport paths and target vector fields for paired noise/data samples.

Conditional OT Paths

Use this skill when a recovery or implementation needs the paper's conditional optimal-transport path from a base sample x0 to a data sample x1 and the corresponding regression target for Conditional Flow Matching. Do not use it to train a neural network or integrate a CNF; those are separate contracts.

Inputs

• Equal-length numeric vectors x0 and x1.
• A time t in [0, 1].
• sigma_min in (0, 1] for the OT variance schedule.

Outputs

• x_t = (1 - (1 - sigma_min)t) x0 + t x1.
• u_t = x1 - (1 - sigma_min) x0.
• Diagnostics for endpoint consistency, finite values, and target invariance.

Workflow

1. Validate vector dimensions and scalar ranges before computing path values.
2. Use scripts/ot_paths.py to compute x_t, u_t, and diagnostics.
3. Treat u_t as the target for a vector-field regressor; do not modify it with downstream loss weighting.
4. Preserve the distinction between the conditional path sample and the marginal CNF trajectory.

Validation

Run:

python tests/test_ot_paths.py
python scripts/ot_paths.py --x0 '[0, 1]' --x1 '[2, 3]' --t 0.5

Limitations

This skill implements the deterministic Gaussian OT-path formulas used for fast proxy validation. It does not estimate marginal vector fields or train image-scale models.

Cycle refinement: invalid times must fail before any recovery harness consumes the path sample.