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name: epsilon_objective description: Compute DDPM epsilon-prediction losses and weighted denoising objective terms for recovery training checks.

Epsilon Objective

Use this skill when a DDPM task needs to score predictions of the Gaussian noise injected by the forward process. It implements the simplified epsilon mean-squared-error objective and a bounded variational-style weighting. Do not use this skill to update model parameters; optimizers belong in a training harness.

Inputs

• True epsilon values used to create x_t.
• Predicted epsilon values from a model or reduced proxy.
• Optional schedule dictionary and one-based timesteps for weighted terms.

Outputs

• mse: mean squared epsilon-prediction error.
• residuals and squared_errors per example.
• Optional weighted_mse and weights when schedule/timesteps are supplied.

Workflow

1. Call epsilon_loss(true_epsilon, predicted_epsilon) for the paper's simplified training objective.
2. Call weighted_epsilon_loss(...) only when a schedule and timesteps are available.
3. Treat exact epsilon prediction as zero loss and any systematic prediction bias as positive loss.
4. Save the returned dictionary in recovery traces when validating reduced training.

Validation

Run python tests/test_epsilon_objective.py or validate the full skill tree with the Distiller validator and --run-tests.

Limitations

The weighted helper uses a deterministic proxy with sigma_t^2 equal to posterior variance when positive, otherwise beta_t. This is sufficient for mechanism checks but not a full likelihood benchmark.