  Invertible flow-based generative models are an effective method for learning
to generate samples, while allowing for tractable likelihood computation and
inference. However, the invertibility requirement restricts models to have the
same latent dimensionality as the inputs. This imposes significant
architectural, memory, and computational costs, making them more challenging to
scale than other classes of generative models such as Variational Autoencoders
(VAEs). We propose a generative model based on probability flows that does away
with the bijectivity requirement on the model and only assumes injectivity.
This also provides another perspective on regularized autoencoders (RAEs), with
our final objectives resembling RAEs with specific regularizers that are
derived by lower bounding the probability flow objective. We empirically
demonstrate the promise of the proposed model, improving over VAEs and AEs in
terms of sample quality.
