We research Variational Rectified Move Matching, a framework that enhances basic rectified circulation matching by modeling multi-modal velocity vector-fields. At inference time, basic rectified circulation matching ‘strikes’ samples from a supply distribution to the goal distribution by fixing an extraordinary differential equation through integration alongside a velocity vector-field. At coaching time, the rate vector-field is learnt by linearly interpolating between coupled samples one drawn from the supply and one drawn from the goal distribution randomly. This results in ”ground-truth” velocity vector-fields that time in several instructions on the identical location, i.e., the rate vector-fields are multi-modal/ambiguous. Nevertheless, since coaching makes use of a regular mean-squared-error loss, the learnt velocity vector-field averages ”ground-truth” instructions and is not multi-modal. In distinction, variational rectified circulation matching learns and samples from multi-modal circulation instructions. We present on artificial information, MNIST, CIFAR-10, and ImageNet that variational rectified circulation matching results in compelling outcomes.
