We present the new bidirectional variational autoencoder (BVAE) network architecture. The BVAE uses a single neural network both to encode and decode instead of an encoder-decoder network pair. The network encodes in the forward direction and decodes in the backward direction through the same synaptic web. Simulations compared BVAEs and ordinary VAEs on the four image tasks of image reconstruction, classification, interpolation, and generation. The image datasets included MNIST handwritten digits, Fashion-MNIST, CIFAR-10, and CelebA-64 face images. The bidirectional structure of BVAEs cut the parameter count by almost 50% and still slightly outperformed the unidirectional VAEs.