SDE are used to model the data distribution of an image

data ⇒ noise in SDE

standard SDE

SDE = dX_t = f(X) * dt + r(t) * W_t

W_t = brownian motion

reverse SDE

SDE = dX_t = [f(X) - g^2(t)*change(log p(x)_t) ] dt + * g(t)W_t

change(log p(x)_t) : gradient or change of prob density

• if the gradient increases, we are converging toward prob that is higher, thus more realistic structures of the data. This means we should be deccelerating our rate of change in X, and therefore reduce the drift term of approaching that value

Scores

basically the gradient of the log probability density): how much the density of a particular image output state’s probability of occuring changes based on some input x

We can create some conditional SDE (where the training does not see it) and it can be estimated under unconditional scores. If scores tell us the change in density or likelihood of some image output occuring

Background

Perturbation kernels: function that describes how noise is added to data. It relates to data distribution

• kernels are used to estimate prob density functions, defines how data is transformed. In this case, how it is perturbed
• Integrating kernel over true data distr

3 SCORE-BASED GENERATIVE MODELING WITH SDES