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.