What is predicted in the common simplified DDPM objective?

Question: In the widely used simplified training objective for a denoising diffusion probabilistic model, a noisy sample is constructed as xₜ = √ᾱₜ x₀ + √(1−ᾱₜ) ε. What is the neural network commonly trained to predict using mean-squared error? A) The particular Gaussian noise ε used to construct xₜ B) The exact reverse-process covariance matrix for every xₜ C) The clean-data likelihood p(x₀) directly D) The timestep posterior q(t|xₜ) from the corrupted sample Correct: A Explanation: The standard simplified objective trains εθ(xₜ,t) to approximate the sampled noise ε. This parameterisation is related to denoising score matching and permits reconstruction of quantities needed for the reverse denoising process. Topic: advanced ML / diffusion models / denoising objective