In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Input: Consider Input: We present a deep generative model, named Monge-Amp\'ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\'ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\'ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\'ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.

Output: A gradient flow based dynamical system for invertible generative modeling

Input: Consider Input: Recent advances in deep generative models have lead to remarkable progress in synthesizing high quality images. Following their successful application in image processing and representation learning, an important next step is to consider videos. Learning generative models of video is a much harder task, requiring a model to capture the temporal dynamics of a scene, in addition to the visual presentation of objects. While recent generative models of video have had some success, current progress is hampered by the lack of qualitative metrics that consider visual quality, temporal coherence, and diversity of samples. To this extent we propose Frechet Video Distance (FVD), a new metric for generative models of video based on FID. We contribute a large-scale human study, which confirms that FVD correlates well with qualitative human judgment of generated videos.

Output: We propose FVD: a new metric for generative models of video based on FID. A large-scale human study confirms that FVD correlates well with qualitative human judgment of generated videos.

Input: Consider Input: Continual learning aims to learn new tasks without forgetting previously learned ones. This is especially challenging when one cannot access data from previous tasks and when the model has a fixed capacity. Current regularization-based continual learning algorithms need an external representation and extra computation to measure the parameters' extit{importance}. In contrast, we propose Uncertainty-guided Continual Bayesian Neural Networks (UCB) where the learning rate adapts according to the uncertainty defined in the probability distribution of the weights in networks. Uncertainty is a natural way to identify extit{what to remember} and extit{what to change} as we continually learn, and thus mitigate catastrophic forgetting. We also show a variant of our model, which uses uncertainty for weight pruning
and retains task performance after pruning by saving binary masks per tasks. We evaluate our UCB approach extensively on diverse object classification datasets with short and long sequences of tasks and report superior or on-par performance compared to existing approaches. Additionally, we show that our model does not necessarily need task information at test time, i.e.~it does not presume knowledge of which task a sample belongs to.
Output: A regularization-based approach for continual learning using Bayesian neural networks to predict parameters' importance