Problems

Training Objective

Medium

Implement the simplified DDPM noise-prediction objective.

L_{\mathrm{simple}} = \frac{1}{N}\sum_{i=1}^{N}\left(\epsilon_i-\epsilon_{\theta,i}\right)^2.

Here, $\epsilon$ is the Gaussian noise used to construct a noisy training sample, $\epsilon_\theta$ is the denoiser's prediction of that noise, and $N$ is the number of scalar values in the batch. Return the mean squared error as a Python float rounded to six decimals.

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Examples

Input: epsilon=[[0.5,-0.3],[0.1,-0.8]], epsilon_pred=[[0,0],[0,0]]

Output: 0.2475

Explanation: The result is the mean of the four squared noise-prediction errors.

Input: epsilon=[[0.5,-0.3],[0.1,-0.8]], epsilon_pred=[[0.5,-0.3],[0.1,-0.8]]

Output: 0.0

Input: epsilon=[[1,-1]], epsilon_pred=[[0.8,-0.7]]

Output: 0.065

Hint 1

Subtract epsilon_pred from epsilon before squaring.

Hint 2

Use np.mean over the complete squared-error array.

Requirements

Use NumPy.
Compute the squared difference between epsilon and epsilon_pred elementwise.
Average across every batch and feature dimension.
Return one nonnegative Python float rounded to six decimals.

Constraints

epsilon and epsilon_pred are equally shaped, nonempty nested lists of real numbers.
Calculations use NumPy float64.

All steps in DDPM

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