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name: reverse_denoising_step description: Convert predicted DDPM epsilon values into reverse-process means and deterministic or stochastic denoising samples.

Reverse Denoising Step

Use this skill when a DDPM recovery needs to apply the paper's epsilon-parameterized reverse Gaussian transition. It converts epsilon_theta(x_t,t) into mu_theta(x_t,t) and optionally adds reverse Gaussian noise. Do not use it to train the epsilon model or to compute image metrics.

Inputs

• Schedule dictionary with betas, alphas, alpha_bars, and optionally posterior_variances.
• Current noisy scalar/list x_t.
• Predicted epsilon scalar/list matching x_t.
• One-based timestep t.
• Optional reverse noise z and variance mode.

Outputs

• Reverse mean value(s) from the DDPM equation.
• Reverse sample value(s), equal to the mean when z is zero or omitted.
• Coefficients used for auditability.

Workflow

1. Build or load a schedule from the diffusion schedule skill.
2. Call reverse_mean(schedule, x_t, predicted_epsilon, t).
3. Call reverse_sample(...) with explicit zero noise for deterministic recovery checks.
4. Record the output in mechanism checks when validating proxy recovery.

Validation

Run python tests/test_reverse_step.py or the Distiller skill-tree validator with --run-tests.

Limitations

The helper validates the reverse mean equation and single-step sampling. It does not claim to reproduce long-chain image generation quality in a bounded recovery run.