---

name: mixed_variable_diffusion_objective description: Encode mixed continuous and categorical variables and compute GSDM-style conditional diffusion denoising losses.

Mixed Variable Diffusion Objective

Use this skill when a GSDM recovery needs deterministic diffusion mechanics for mixed continuous and discrete variables: one-hot categorical encoding, arbitrary observation masks, forward noising, decoding, and masked x0 denoising loss.

Do not use this skill as a full neural diffusion implementation. It supplies the objective contract and small numerical helpers used by recovery and tests.

Inputs

• Variable specs with name, kind, and optional num_categories.
• Values for each variable.
• Beta schedule and timestep.
• Noise vector.
• Prediction vector and optional loss mask.

Outputs

• Encoded x0 vector.
• Noisy xt vector.
• Observation mask expanded to encoded dimensions.
• Masked mean-squared denoising loss.
• Decoded categorical values by argmax.

Workflow

1. Encode continuous values as scalar channels.
2. Encode categorical values as one-hot channel blocks.
3. Expand observed variable names to encoded dimensions.
4. Compute alpha_bar_t from the beta schedule.
5. Produce xt = sqrt(alpha_bar_t) * x0 + sqrt(1 - alpha_bar_t) * noise.
6. Compute masked MSE over latent dimensions.

CLI

python scripts/diffusion_objective.py --demo --output /tmp/gsdm_objective.json

Validation

python -m pytest tests

The tests cover categorical round-trips, the noising equation, and masked loss behavior.

Limitations

The helpers use Python lists and floats for portability. They are intended for small recovery checks, not high-throughput training.