This paper introduces a Variational Recurrent Neural Network (VRNN) for modeling sequential data by incorporating latent random variables into the hidden state of a recurrent neural network (RNN). The VRNN extends the variational autoencoder (VAE) to a recurrent framework, allowing it to model complex, high-dimensional sequences such as natural speech and handwriting. The key idea is to introduce latent random variables that capture the variability in the data, enabling the model to better represent the complex dependencies observed in structured sequences. The VRNN differs from standard RNNs in that it explicitly models the dependencies between latent random variables across time steps. This is achieved by conditioning the prior distribution of the latent variables on the RNN's hidden state, which allows the model to capture temporal structure in the data. The VRNN is trained using a variational lower bound, which includes both the KL divergence between the approximate posterior and the true prior, and the log-likelihood of the data given the latent variables. The paper evaluates the VRNN on four speech datasets and one handwriting dataset, demonstrating that it outperforms standard RNN-based models in terms of log-likelihood and generates more realistic samples. The VRNN is particularly effective in modeling sequences with high signal-to-noise ratios and complex dependencies, such as natural speech. The results show that the inclusion of latent random variables significantly improves the model's ability to capture the variability in the data, leading to better performance in both speech and handwriting generation tasks. The VRNN is shown to be more effective than standard RNNs in modeling sequences with complex dependencies, as it can capture the temporal structure of the data through the latent variables. The model is also able to generate more diverse and consistent handwriting samples, maintaining a consistent writing style throughout the generated sequence. The paper concludes that the VRNN provides a powerful framework for modeling structured sequential data, particularly in applications such as speech and handwriting generation.This paper introduces a Variational Recurrent Neural Network (VRNN) for modeling sequential data by incorporating latent random variables into the hidden state of a recurrent neural network (RNN). The VRNN extends the variational autoencoder (VAE) to a recurrent framework, allowing it to model complex, high-dimensional sequences such as natural speech and handwriting. The key idea is to introduce latent random variables that capture the variability in the data, enabling the model to better represent the complex dependencies observed in structured sequences. The VRNN differs from standard RNNs in that it explicitly models the dependencies between latent random variables across time steps. This is achieved by conditioning the prior distribution of the latent variables on the RNN's hidden state, which allows the model to capture temporal structure in the data. The VRNN is trained using a variational lower bound, which includes both the KL divergence between the approximate posterior and the true prior, and the log-likelihood of the data given the latent variables. The paper evaluates the VRNN on four speech datasets and one handwriting dataset, demonstrating that it outperforms standard RNN-based models in terms of log-likelihood and generates more realistic samples. The VRNN is particularly effective in modeling sequences with high signal-to-noise ratios and complex dependencies, such as natural speech. The results show that the inclusion of latent random variables significantly improves the model's ability to capture the variability in the data, leading to better performance in both speech and handwriting generation tasks. The VRNN is shown to be more effective than standard RNNs in modeling sequences with complex dependencies, as it can capture the temporal structure of the data through the latent variables. The model is also able to generate more diverse and consistent handwriting samples, maintaining a consistent writing style throughout the generated sequence. The paper concludes that the VRNN provides a powerful framework for modeling structured sequential data, particularly in applications such as speech and handwriting generation.