  This paper introduces the Procedural (audio) Variational autoEncoder (ProVE)
framework as a general approach to learning Procedural Audio PA models of
environmental sounds with an improvement to the realism of the synthesis while
maintaining provision of control over the generated sound through adjustable
parameters. The framework comprises two stages: (i) Audio Class Representation,
in which a latent representation space is defined by training an audio
autoencoder, and (ii) Control Mapping, in which a joint function of
static/temporal control variables derived from the audio and a random sample of
uniform noise is learned to replace the audio encoder. We demonstrate the use
of ProVE through the example of footstep sound effects on various surfaces. Our
results show that ProVE models outperform both classical PA models and an
adversarial-based approach in terms of sound fidelity, as measured by Fr\'echet
Audio Distance (FAD), Maximum Mean Discrepancy (MMD), and subjective
evaluations, making them feasible tools for sound design workflows.
