We propose a hybrid deep learning model that merges Variational Autoencoders and Convolutional LSTM Networks (VAE-ConvLSTM) to forecast inflation. Using a public macroeconomic database that comprises 134 monthly US time series from January 1978 to December 2019, the proposed model is compared against several popular econometric and machine learning benchmarks, including Ridge regression, LASSO regression, Random Forests, Bayesian methods, VECM, and multilayer perceptron. We find that VAE-ConvLSTM outperforms the competing models in terms of consistency and out-of-sample performance. The robustness of such conclusion is ensured via cross-validation and Monte-Carlo simulations using different training, validation, and test samples. Our results suggest that macroeconomic forecasting could take advantage of deep learning models when tackling nonlinearities and nonstationarity, potentially delivering superior performance in comparison to traditional econometric approaches based on linear, stationary models.