which resembles denoising score matching over multiple noise scales indexed by t [55]. As Eq. (12)
is equal to (one term of) the variational bound for the Langevin-like reverse process (11), we see
that optimizing an objective resembling denoising score matching is equivalent to using variational
inference to ﬁt the ﬁnite-time marginal of a sampling chain resembling Langevin dynamics.
To summarize, we can train the reverse process mean function approximator µθ to predict ˜µt, or by
modifying its parameterization, we can train it to predict (cid:15). (There is also the possibility of predicting
x0, but we found this to lead to worse sample quality early in our experiments.) We have shown that
the (cid:15)-prediction parameterization both resembles Langevin dynamics and simpliﬁes the diffusion
model’s variational bound to an objective that resembles denoising score matching. Nonetheless,
it is just another parameterization of pθ(xt−1|xt), so we verify its effectiveness in Section 4 in an
Denoising Diffusion Probabilistic Models