Variational Auto-Encoder (VAE) has been widely adopted in text generation. Among many variants, recurrent VAE learns token-wise latent variables with each conditioned on the preceding ones, which captures sequential variability better in the era of RNN. However, it is unclear how to incorporate such recurrent dynamics into the recently dominant Transformer due to its parallelism. In this work, we propose TRACE, a Transformer-based recurrent VAE structure. TRACE imposes recurrence on segment-wise latent variables with arbitrarily separated text segments and constructs the posterior distribution with residual parameterization. Besides, we design an acceleration method by approximating idempotent matrices, which allows parallelism while maintaining the conditional dependence of latent variables. We demonstrate that TRACE could enhance the entanglement of each segment and preceding latent variables and deduce a non-zero lower bound of the KL term, providing a theoretical guarantee of generation diversity. Experiments on two unconditional and one conditional generation tasks show that TRACE achieves significantly improved diversity while maintaining satisfactory generation quality.
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