Flux inversion is the process by which sources and sinks of a gas are identified from observations of gas mole fraction. The inversion often involves running a Lagrangian particle dispersion model (LPDM) to generate simulations of the gas movement over a domain of interest. The LPDM must be run backward in time for every gas measurement, and this can be computationally prohibitive. To address this problem, here we develop a novel spatio-temporal emulator for LPDM sensitivities that is built using a convolutional variational autoencoder (CVAE, a two-piece neural network capable of condensing and reconstructing images). With the encoder segment of the CVAE, we obtain approximate (variational) posterior distributions over latent variables in a low-dimensional space. We then use a spatio-temporal Gaussian process emulator on the low-dimensional space to emulate new variables at prediction locations and time points. Emulated variables are then passed through the decoder segment of the CVAE