Stochastic Adversarial Video Prediction
Being able to predict what may happen in the future requires an in-depth understanding of the physical and causal rules that govern the world. A model that is able to do so has a number of appealing applications, from robotic planning to representation learning. However, learning to predict raw future observations, such as frames in a video, is exceedingly challenging -- the ambiguous nature of the problem can cause a naively designed model to average together possible futures into a single, blurry prediction. Recently, this has been addressed by two distinct approaches: (a) latent variational variable models that explicitly model underlying stochasticity and (b) adversarially-trained models that aim to produce naturalistic images. However, a standard latent variable model can struggle to produce realistic results, and a standard adversarially-trained model underutilizes latent variables and fails to produce diverse predictions. We show that these distinct methods are in fact complementary. Combining the two produces predictions that look more realistic to human raters and better cover the range of possible futures. Our method outperforms prior and concurrent work in these aspects.READ FULL TEXT VIEW PDF
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Stochastic Adversarial Video Prediction
When we interact with objects in our environment, we can easily imagine the consequences of our actions: push on a ball and it will roll; drop a vase and it will break. The ability to imagine future outcomes provides an appealing avenue for learning about the world. Unlabeled video sequences can be gathered autonomously with minimal human intervention, and a machine that learns to accurately predict future events will have gained an in-depth and functional understanding of its physical environment. This leads naturally to the problem of video prediction—given a sequence of context frames, and optionally a proposed action sequence, generate the raw pixels of the future frames. Once trained, such a model could be used to determine which actions can bring about desired outcomes [3, 4]
. Unfortunately, accurate and naturalistic video prediction remains an open problem, with state-of-the-art methods producing high-quality predictions only a few frames into the future. One major challenge in video prediction is the ambiguous nature of the problem. While frames in the immediate future can be extrapolated with high precision, the space of possibilities diverges beyond a few frames, and the problem becomes multimodal by nature. Methods that use deterministic models and loss functions unequipped to handle this inherent uncertainty, such as mean-squared error (MSE), will average together possible futures, producing blurry predictions. Prior and concurrent  work has explored stochastic models for video prediction, using the framework of variational autoencoders (VAEs) 
. These models predict possible futures by sampling latent variables. During training, they optimize a variational lower bound on the likelihood of the data in a latent variable model. However, the posterior is still a pixel-wise MSE loss, corresponding to the log-likelihood under a fully factorized Gaussian distribution. This makes training tractable, but causes them to still make blurry and unrealistic predictions when the latent variables alone do not adequately capture the uncertainty. Another relevant branch of recent work has been generative adversarial networks (GANs)
for image generation. Here, a generator network is trained to produce images that are indistinguishable from real images, under the guidance of a learned discriminator network trained to classify images as real or generated. The learned discriminator operates on patches or entire images, and is thus capable of modeling the joint distribution of the generated pixels, without making any independence assumptions. Although this overcomes the limitations of pixel-wise losses, GANs are notoriously susceptible to mode collapse, where latent random variables are often ignored by the model, especially in the conditional setting[7, 8, 9, 10]. This makes them difficult to apply to generation of diverse and plausible futures, conditioned on context frames. A handful of recent works have explored video prediction and generation with GANs, typically with models that are either deterministic [7, 11, 12, 13], not conditioned on context images (and therefore applicable only to unconditional generation, rather than prediction) [14, 15], or incorporate stochasticity only through input noise [16, 17]
. As we illustrate in our experiments, GANs without an explicit latent variable interpretation are prone to mode collapse and do not generate diverse futures. To address these challenges, we propose a model that combines both adversarial losses and latent variables to enable high-quality stochastic video prediction. Our model consists of a video prediction network that can sample multiple plausible futures by sampling time-varying stochastic latent variables and decoding them into multiple frames. At training time, an inference network estimates the distribution of these latent variables, and video discriminator networks classify generated videos from real. The full training objective is the variational lower bound used in VAEs combined with the adversarial loss used in GANs. This enables to capture stochastic posterior distributions of videos while also modeling the spatiotemporal joint distribution of pixels. This formalism, referred to as VAE-GANs, was originally proposed for image generation
and recently used in the conditional setting of multimodal image-to-image translation
. To our knowledge, our work is the first to extend this approach to stochastic video prediction. A recurring challenge in video prediction is the choice of evaluation metric. While simple quantitative metrics such as the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index provide appealing ways to measure the differences between various methods, they are known to correspond poorly to human preferences [20, 21]. In fact, SSIM was not designed for situations where spatial ambiguities are a factor . Indeed, in our quantitative comparisons, we show that these metrics rarely provide accurate cues as to the relative ordering of the various methods in terms of prediction quality. We include a detailed ablation analysis of our model and its design decisions on these standard metrics, in comparison with prior work. We also present an evaluation on a “Visual Turing test”, using human judgments via the two-alternative forced choice (2AFC) method, which shows that the best models according to human raters are generally not those that excel on the standard metrics. In addition, we use a perceptual distance metric [23, 24, 21] to assess the diversity of the output videos, and also as an alternative to the standard full-reference metrics used in video prediction. The primary contribution of our work is an stochastic video prediction model, based on VAE-GANs. To our knowledge, this is the first stochastic video prediction model in the literature that combines an adversarial loss with a latent variable model trained via the variational lower bound. Our experiments show that the VAE component greatly improves the diversity of the generated images, while the adversarial loss attains prediction results that are substantially more realistic than both prior  and concurrent  (e.g. see Fig. 1). We further present a systematic comparison of various types of prediction models and losses, including VAE, GAN, and VAE-GAN models, and analyze the impact of these design decisions on image realism, prediction diversity, and accuracy.
Recent developments in expressive generative models based on deep networks has led to impressive developments in video generation and prediction. Prior methods vary along two axes: the design of the generative model and training objective. Earlier approaches to prediction focused on models that generate pixels directly from the latent state of the model using both feedforward [25, 7] and recurrent [26, 27] architectures. An alternative to generating pixels is transforming them by applying a constrained geometric distortion to a previous frame [3, 28, 29, 30, 11, 31, 32, 16, 13, 33, 34, 35]. These methods can potentially focus primarily on motion, without explicitly reconstructing appearance. Aside from the design of the generator architecture, performance is strongly affected by the training objective. Simply minimizing mean squared error can lead to good predictions for deterministic synthetic videos, such as video game frames [26, 36]. However, on real-world videos that contain ambiguity and uncertainty, this objective can result in blurry predictions, as the model averages together multiple possible futures to avoid incurring a large squared error 
. Incorporating uncertainty is critical for addressing this issue. One approach is to model the full joint distribution using pixel-autoregressive models[37, 38], which can produce sharp images, though training and inference are impractically slow, even with parallelism . Another approach is to train a latent variable model, such as in variational autoencoders (VAEs) . Conditional VAEs have been used for prediction of optical flow trajectories , single-frame prediction , and very recently for stochastic multi-frame video prediction . Concurrent with our work, Denton et al. proposed an improved VAE-based model that can synthesize physically plausible futures for longer horizons . While these models can model distributions over possible futures, the prediction distribution is still fully factorized over pixels, which still tends to produce blurry predictions. Our experiments present a detailed comparison to recent prior  and concurrent  methods. The basic VAE-based version of our method slightly outperforms Denton et al.  in human subjects comparisons, and substantially outperforms all methods, including , when augmented with an adversarial loss. Adversarial losses in generative adversarial networks (GANs) for image generation can produce substantially improved realism . However, adversarial loss functions tend to be difficult to tune, and these networks are prone to the mode collapse problem, where the generator fails to adequately cover the space of possible predictions and instead selects one or a few prominent modes. A number of prior works have used adversarial losses for deterministic video prediction [7, 11, 12, 13, 40, 41]. Liang et al.  proposed to combine a stochastic model with an adversarial loss, but the proposed optimization does not optimize a latent variable model, and the latent variables are not sampled from the prior at test-time. In contrast, models that incorporate latent variables via a variational bound (but do not include an adversarial loss) use an encoder at training-time that performs inference from the entire sequence, and then sample the latents from the prior at test-time [1, 2]. Several prior works have also sought to produce unconditioned video generations [14, 15, 17] and conditional generation with input noise [16, 17]. In our comparison, we show that a GAN model with input noise can indeed generate realistic videos, but fails to adequately cover the space of possible futures. In contrast, our approach, which combines VAE-based latent variable models with an adversarial loss, produces predictions that are both visually plausible and highly diverse. Evaluating the performance of video prediction methods is a major challenge. Standard quantitative metrics, such as PSNR and SSIM , provide a convenient score for comparison, but do not equate to the qualitative rankings provided by human raters, as discussed in  and illustrated in our evaluation. The success of these methods can also be evaluated indirectly, such as evaluating the learned representations [42, 43, 44], or using the predictions for planning actions of a robotic system in the real world [45, 4, 46]. We argue that it is difficult to quantify the quality of video prediction with a single metric, and instead propose to use a combination of quantitative metrics that include subjective human evaluations, and automated measures of prediction diversity and accuracy. Our experiments show that VAE-based latent variable models are critical for prediction diversity, while adversarial losses contribute the most to realism, and we therefore propose to combine these two components to produce predictions that both cover the range of possible futures and provide realistic images.
Our goal is to learn an stochastic video prediction model that can predict videos that are diverse and perceptually realistic, and where all predictions are plausible futures for the given initial image. In practice, we use a short initial sequence of images (typically two frames), though we will omit this in our derivation for ease of notation. Our model consists of a recurrent generator network , which is a deterministic video prediction model that maps an initial image and a sequence of latent random codes , to the predicted sequence of future images . Intuitively, the latent codes encapsulate any ambiguous or stochastic events that might affect the future. At test time, we sample videos by first sampling the latent codes from a prior distribution , and then passing them to the generator. We use a fixed unit Gaussian prior, . The training procedure for this includes elements of variational inference and generative adversarial networks. Before describing the training procedure, we formulate the problem in the context of VAEs and GANs.
Our recurrent generator predicts each frame given the previous frame and a random latent code. The previous frames passed to the generator are either the ground truth frames, when available (i.e. the initial sequence of images), or the previous predicted frames. The generator specifies a distribution
, and it is parametrized as a fixed-variance Laplacian distribution with the mean given by. The likelihood of the data cannot be directly maximized, since it involves marginalizing over the latent variables, which is intractable in general. Thus, we instead maximize the variational lower bound of the log-likelihood. We approximate the posterior with a recognition model , which is parametrized as a conditionally Gaussian distribution , represented by a deep network . The encoder is conditioned on the frames of the adjacent time steps to allow the latent variable to encode any ambiguous information of the transition between frames and . During training, the latent code is sampled from . The generation of each frame can be thought of as the reconstruction of frame , where the ground truth frame (along with ) is encoded into a latent code , and then it (along with the last frame) is mapped back to . Since the latent code has ground truth information of the frame being reconstructed, the model is encouraged to use it during training. This is a conditional version of the variational autoencoder (VAEs) , where the encoder and decoder are conditioned on the previous frame ( or ). To allow back-propagation through the encoder, the reconstruction term is rewritten using the re-parametrization trick ,
To enable sampling from the prior at test time, a regularization term encourages the approximate posterior to be close to the prior distribution,
The VAE optimization involves minimizing the following objective, where the relative weighting of and is determined by the (fixed) variance of the Laplacian distribution,
Without overcoming the problem of modeling pixel covariances, it is likely not possible to produce sharp and clean predictions. Indeed, as shown in our experiments, the pure VAE model tends to produce blurry futures. We can force the predictions to stay on the video manifold by matching the distributions of predicted and real videos. Given a classifier that is capable of distinguishing generated videos from real videos , the generator can be trained to match the statistics of the real data distribution using the binary cross-entropy loss,
The classifier, which is not known a priori and is problem-specific, can be realized as a deep discriminator network that can be adversarially learned,
This is the setting of generative adversarial networks (GANs) . In the conditional case, a per-pixel reconstruction term is added to the objective, which is analogous to , except that the latent codes are sampled from the prior.
The VAE and GAN models provide complementary strengths. GANs use a learned loss function through the discriminator, which learns the statistics of natural videos. However, GANs can suffer from the problem of mode collapse, especially in the conditional setting [9, 8, 10]. VAEs explicitly encourage the latent code to be more expressive and meaningful, since the learned encoder produces codes that are useful for making accurate predictions at training time. However, during training, VAEs only observe latent codes that are encodings of ground truth images, and never train on completely randomly drawn latent codes, leading to a potential train and test mismatch. GANs, however, are trained with randomly drawn codes. Our stochastic adversarial video prediction (SAVP) model combines both approaches, shown in Fig. 2. Another term is introduced, which is analogous to except that it uses latent codes sampled from and a separate video discriminator . The objective of our SAVP model is
Our model is inspired by VAE-GANs  and BicycleGAN , which have shown promising results in the conditional image generation domain, but have not been applied to video prediction. The video prediction setting presents two important challenges. First, conditional image generation can handle large appearance changes between the input and output, but suffer when attempting to produce large spatial changes. The video prediction setting is precisely the opposite—the appearance remains largely the same from frame to frame, but the most important changes are spatial. Secondly, video prediction involves sequential prediction. To help solve this, modifications can be made to the architecture, such as adding recurrent layers within the generator and using a video-based discriminator to model dynamics. However, errors in the generated images can easily accumulate, as they are repeatedly fed back into the generator in an autoregressive approach. Our approach is the first to use VAE-GANs in a recurrent setting for stochastic video prediction.
The generator is a convolutional LSTM [27, 47] that predicts pixel-space transformations between the current and next frame, with additional skip connections with the first frame as done in SNA . At every time step, the network is conditioned on the current frame and latent code. After the initial frames, the network is conditioned on its own predictions. The conditioning on the latent codes is realized by concatenating them along the channel dimension to the inputs of all the convolutional layers of the convolutional LSTM. The encoder is a feed-forward convolutional network that encodes pairs of images at every time step. The video discriminator is a feed-forward convolutional network with 3D filters, based on SNGAN  but with the filters “inflated” from 2D to 3D. See Appendix 0.A for additional details on the network architectures and training procedure.
Our experimental evaluation studies the realism, diversity, and accuracy of the videos generated by our approach and prior methods, evaluate the importance of various design decisions, including the form of the reconstruction loss and the presence of the variational and adversarial objectives. Evaluating the performance of stochastic video prediction models is exceedingly challenging: not only should the samples from the model be physically realistic and visually plausible given the context frames, but the model should also be able to produce diverse samples that match the conditional distribution in the data. These properties are difficult to evaluate precisely: realism is not accurately reflected with simple metrics of reconstruction accuracy, and the true conditional distribution in the data is unknown, since real-world datasets only have a single future for each initial sequence. Below, we discuss the metrics that we use to evaluate realism, diversity, and accuracy. No single metric alone provides a clear answer as to which model is better, but considering multiple metrics can provide us with a more complete understanding of the performance and trade-offs of each approach.
The realism of the predicted videos is evaluated based on a real vs. fake two-alternative forced choice (2AFC) test. Human judges on Amazon Mechanical Turk (AMT) are presented with a pair of videos—one generated and one real—and asked to identify the generated, or “fake” video. We use the implementation from , modified for videos. Each video is 10 frames long and shown over 2.5 seconds. For each method, we gather 1000 judgments from 25 human judges. Each human evaluator is provided with 10 training trials followed by 40 test trials. A method that produces perfectly realistic videos would achieve a fooling rate of .
Realism is not the only factor in determining the performance of a video prediction model: aside from generating predictions that look physically plausible and realistic, a successful model must also be able to adequately cover the range of possible futures in an uncertain environment. We compute diversity as the average distance between randomly sampled video predictions, similar to 
. Distance is measured in the VGG feature space (pretrained on ImageNet classification), averaged across five layers, which has been shown to correlate well with human perception[23, 24, 21].
One weakness of the above metric is that the samples may be diverse but still not cover the feasible output space. Though we do not have the true output distribution, we can still leverage the single ground truth instance. This can be done by sampling the model a finite number of times, and evaluating the similarity between the best sample and the ground truth. This has been explored in prior work on stochastic video prediction [1, 2]
, using PSNR or SSIM as the evaluation metric. In addition to these, we use cosine similarity in the pretrained VGG feature space.
We evaluate on two real-world datasets: the BAIR action-free robot pushing dataset  and the KTH human actions dataset . See Sec. 0.B.3 for additional results on the action-conditioned version of the robot pushing dataset.
This dataset consists of a randomly moving robotic arm that pushes objects on a table . This dataset is particularly challenging since (a) it contains large amounts of stochasticity due to random arm motion, and (b) it is a real-world application, with a diverse set of objects and large cluttered scene (rather than a single frame-centered object with a neutral background). The videos have a spatial resolution of . We condition on the first 2 frames and train to predict the next 10 frames. We predict 10 future frames for the 2AFC experiments and 28 future frames for the other experiments.
This dataset consists of a human subject doing one of six activities: walking, jogging, running, boxing, hand waving, and hand clapping . For the first three activities, the human enters and leaves the frame multiple times, leaving the frame empty with a mostly static background for multiple frames at a time. The sequences are particularly stochastic when the initial frames are all empty since the human can enter the frame at any point in the future. As a preprocessing step, we center-crop each frame to a square and then resize to a spatial resolution of . We condition on the first 10 frames and train to predict the next 10 frames. We predict 10 future frames for the 2AFC experiments and 30 future frames for the other experiments. For each sequence, subclips of the desired length are randomly sampled at training and test time.
We compare the following variants of our method, in our effort to evaluate the effect of each loss term. Code and models are available at our website111https://alexlee-gk.github.io/video_prediction. Ours, SAVP. Our full stochastic adversarial video prediction model, with the VAE and GAN objectives shown in Fig. 2 and in Eq. (missing). Ours, GAN-only. An ablation of our model with only a conditional GAN, without the variational autoencoder. This model still takes a noise sample as input, but the noise is sampled from the prior during training. This model is broadly representative of prior stochastic GAN-based methods [14, 15, 16, 17]. Ours, VAE-only. An ablation of our model with only a conditional VAE, with the reconstruction loss but without the adversarial loss. This model is broadly representative of prior stochastic VAE-based methods [1, 2]. We also compare to the following prior and concurrent stochastic VAE-based methods, both of which use the reconstruction loss and no adversarial loss. Stochastic Variational Video Prediction (SV2P). A VAE-based method proposed by Babaeizadeh et al. . To our knowledge, this is the most recent prior VAE-based method, except for the concurrent method  discussed below. Stochastic Video Generation with a Learned Prior (SVG-LP). This is a concurrent VAE-based method proposed by Denton et al. , with learned priors for the latent codes, that shows results that outperform Babaeizadeh et al. . See Sec. 0.B.2 for qualitative results on representative prior work of an unconditioned GAN-based method, MoCoGAN .
model, based on VAE-GANs, improves along the realism axis compared to a pure VAE method, and improves along the diversity axis compared to a pure GAN method. Although the SV2P methods mode-collapse on the KTH dataset, we note that they did not evaluate on this dataset, and their method could benefit from hyperparameters that are better suited for this dataset.
In Fig. 5, variants of our method are compared to prior work. On the BAIR action-free dataset, our GAN variant achieves the highest fooling rate, whereas our proposed SAVP model, a VAE-GAN-based method, achieves a fooling rate that is roughly halfway between the GAN and VAE models alone. The SV2P method  does not achieve realistic results. The concurrent VAE-based SVG-LP method  achieves high realism, similar to our VAE variant, but substantially below our GAN-based variants. On the KTH dataset, our SAVP model achieves the highest realism score, substantially above our GAN variant. Among the VAE-based methods without adversarial losses, our VAE-only model outperforms prior SV2P  and concurrent SVG-FP  methods in terms of realism.
We measure diversity by taking the distance between random samples. Diversity results are also shown in Fig. 5 and a qualitative visualization of diversity is shown in Fig. 6. While the GAN-only approach achieves realistic results, it shows lower diversity than the VAE-based methods. This is an example of the commonly known phenomenon of mode-collapse, where multiple latent codes produce the same or similar images on the output . Intuitively, the VAE-based methods explicitly encourage the latent code to be more expressive by using an encoder from the output space into the latent space during training. This is verified in our experiments, as the VAE-based variants, including our SAVP model, achieve higher diversity than our GAN-only models on both datasets. On the KTH dataset, our VAE variant and concurrent VAE-based SVG-FP method  both achieve significantly higher diversity than all the other methods. Although the VAE-based SV2P methods  mode-collapse on the KTH dataset, we note that they did not evaluate on this dataset, and as such, their method could benefit from different hyperparameters that are better suited for this dataset.
Following recent work on VAE-based video prediction [1, 2], we evaluate on full-reference metrics by sampling multiple predictions from the model. We draw 100 samples for each video, find the “best” sample by computing similarity to the ground truth video, and show the average similarity across the test set as a function of time. The results on the BAIR and KTH datasets are shown in Fig. 7 and Fig. 8, respectively. We test generalization ability by running the model for more time steps than it was trained for. Even though the model is only trained to predict 10 future frames, we observe graceful degradation over time. While PSNR and SSIM  are commonly used for video prediction, these metrics are not necessarily indicative of prediction quality. In video prediction, structural ambiguities and geometric deformations are a dominant factor, and SSIM is not an appropriate metric in such situations [22, 21]. This is particularly noticeable with the SV2P method, which achieves high PSNR and SSIM scores, but produces blurry and unrealistic images. Furthermore, we additionally trained our VAE and deterministic variants using the standard MSE loss to understand the relationship between the form of the reconstruction loss and the metrics. The general trend is that models trained with , which favors blurry predictions, are better on PSNR and SSIM, but models trained with are better on VGG cosine similarity. See Sec. 0.B.1 for quantitative results comparing models trained with and
. In addition, we expect for our GAN-based variants to underperform on PSNR and SSIM since GANs prioritize matching joint distributions of pixels over per-pixel reconstruction accuracy. To partially overcome the limitations of these metrics, we also evaluate using distances in a deep feature space[23, 24], which have been shown to correspond better with human perceptual judgments . We use cosine similarity between VGG features averaged across five layers. Notice that this VGG similarity is a held-out metric, meaning that it was not used as a loss function during training. Otherwise, a model trained for it would unfairly and artificially achieve better similarities by exploiting potential flaws on that metric. Our VAE variant, along with concurrent VAE-based SVG method , performs best on this metric. Our SAVP model achieves slightly lower VGG similarity, striking a desirable balance in predicting videos that are realistic, diverse, and accurate. Among the VAE-based methods, prior SV2P method  achieves the lowest VGG similarity. On stochastic environments, such as in the BAIR action-free dataset, there is some correlation between diversity and accuracy of the best sample: a model with diverse predictions is more likely to sample a video that is close to the ground truth. This relation can be seen in Fig. 5 and Fig. 7 for the robot dataset, e.g. our SAVP model is both more diverse and achieves higher similarity than our GAN-only variant. This is not true on less stochastic environments. We hypothesize that the KTH dataset is not as stochastic when conditioning on 10 frames, as evidenced by the fact that the similarities of the deterministic and stochastic models are not that far apart from each other. This would explain why our GAN variant and SV2P achieve modest similarities despite achieving low diversity on the KTH dataset.
The GAN alone achieves high realism but low diversity. The VAE alone achieves lower realism but provides increased diversity. Adding the GAN to the VAE model increases the realism without sacrificing diversity, at only a small or no cost in realism on stochastic datasets. This is consistent with , which showed that combining GAN and VAE-based models can provide benefits in the case of image generation. To our knowledge, our method is the first to extend this class of models to the stochastic video prediction setting, and the first to illustrate that this leads to improved realism with a degree of diversity comparable to the best VAE models in stochastic environments. The results show that this combination of losses is the best choice for realistic coverage of diverse stochastic futures.
In this work, we proposed a video prediction model that combines latent variables trained via a variational lower bound with an adversarial loss to produce a high degree of visual and physical realism. The VAE-style training with latent variables enables our method to make diverse stochastic predictions, and our experiments show that the adversarial loss is effective at producing predictions that are more visually realistic according to human raters. Evaluation of video prediction models is a major challenge, and we evaluate our method, as well as ablated variants that consist of only the VAE or only the GAN loss, in terms of a variety of quantitative and qualitative measures, including human ratings, diversity, and accuracy of the predicted samples. Our results demonstrate that our approach produces more realistic predictions than prior methods, while preserving the sample diversity of VAE-based methods.
We thank Emily Denton for providing pre-trained models and extensive and timely assistance with reproducing the SVG results, and Mohammad Babaeizadeh for providing data for comparisons with SV2P. This research was supported in part by the Army Research Office through the MAST program, the National Science Foundation through IIS-1651843 and IIS-1614653, and hardware donations from NVIDIA. Alex Lee and Chelsea Finn were also supported by the NSF GRFP. Richard Zhang was partially supported by the Adobe Research Fellowship.
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Our generator network, shown in Fig. 9, is inspired by the convolutional dynamic neural advection (CDNA) model proposed by . The video prediction setting is a sequential prediction problem, so we use a convolutional LSTM [47, 27] to predict future frames. We initialize the prediction on the initial sequence of ground truth frames (2 or 10 frames for the BAIR and KTH datasets, respectively), and predict 10 future frames. The model predicts a sequence of future frames by repeatedly making next-frame predictions and feeding those predictions back to itself. For each one-step prediction, the network has the freedom to choose to copy pixels from the previous frame, used transformed versions of the previous frame, or to synthesize pixels from scratch. The transformed versions of the frame are produced by convolving in the input image with predicted convolutional kernels, allowing for different shifted versions of the input. In more recent work, the first frame of the sequence is also given to the compositing layer . To enable stochastic sampling, the generator is also conditioned on time-varying latent codes, which are sampled at training and test time. Each latent code
is an 8-dimensional vector. At each prediction step, the latent code is passed through a fully-connected LSTM to facilitate correlations in time of the latent variables. The encoded latent code is then passed to all the convolutional layers of the main network, by concatenating it along the channel dimension to the inputs of these layers. Since they are vectors with no spatial dimensions, they are replicated spatially to match the spatial dimensions of the inputs. We made a variety of architectural improvements to the original CDNA and SNA  models, which overall produced better results on the per-pixel loss and similarity metrics. See Fig. 13 for a quantitative comparison of our deterministic variant (without VAE or GAN losses) to the SNA model on the BAIR action-conditioned dataset. Each convolutional layer is followed by instance normalization 
and ReLU activations. We also use instance normalization on the LSTM pre-activations (i.e., the input, forget, and output gates, as well as the transformed and next cell of the LSTM). In addition, we modify the spatial downsampling and upsampling mechanisms. Standard subsampling and upsampling between convolutions is known to produce artifacts for dense image generation tasks[53, 54, 55]
. In the encoding layers, we reduce the spatial resolution of the feature maps by average pooling, and in the decoding layers, we increase the resolution by using bilinear interpolation. All convolutions in the generator use a stride of 1. In the case of the action-conditioned dataset, actions are concatenated to the inputs of all the convolutional layers of the main network, as opposed to only the bottleneck.
The encoder is a standard convolutional network that, at every time step, encodes a pair of images and into and . The same encoder network with shared weights is used at every time step. The encoder architecture consists of three convolutional layers, followed by average pooling of all the spatial dimensions. Two separate fully-connected layers are then used to estimate and , respectively. The convolutional layers use instance normalization, leaky ReLU non-linearities, and stride 2. This encoder architecture is the same one used in BicyleGAN  except that the inputs are pair of images, concatenated along the channel dimension.
The discriminator is a 3D convolutional neural network that takes in all the images of the video at once. We use spectral normalization and the SNGAN discriminator architecture, except that we “inflate” the convolution filters from 2D to 3D. The two video discriminators, and , share the same architecture, but not the weights, as done in BicycleGAN .
Our generator network uses scheduled sampling during training as in Finn et al. , such that at the beginning the model is trained for one-step predictions, while by the end of training the model is fully autoregressive. We trained all models with Adam  for 300000 iterations, linearly decaying the learning rate to 0 for the last 100000 iterations. The same training schedule was used for all the models, except for SVG, which was trained by its author. Our GAN-based variants used an optimizer with , , learning rate of , and a batch size of 16. Our deterministic and VAE models (including SNA and SV2P from prior work) used an optimizer with , , learning rate of , and a batch size of 32. We used for our GAN-based variants, and for all the other models. For our VAE-based variants, we linearly anneal the weight on the KL divergence term from 0 to the final value during training, as proposed by Bowman et al. , from iterations 50000 to 100000. We used a relative weighting of for the BAIR robot pushing datasets, and for the KTH dataset. This hyperparameter was empirically chosen by computing similarity metrics on the validation set.
We train our deterministic and VAE variants with the and losses to compare the effects of these reconstruction losses on the full-reference metrics used in this work. The pixel-wise loss assumes that pixels are generated according to a fully factorized Laplacian distribution, whereas the loss corresponds to a fully factorized Gaussian distribution. See Fig. 10 and Fig. 13 for quantitative results on the action-free and action-conditioned BAIR datasets, respectively. The general trend is that models trained with the loss tend to generate blurry predictions but achieve higher PSNR scores than equivalent models trained with the loss. This is because PSNR and are closely related, the former being a logarithmic function of the latter. The opposite is true for the VGG cosine similarity metric, which has been shown to correspond better with human perceptual judgments . Models trained with significantly outperforms equivalent models trained with . On the SSIM metric, models trained with achieve roughly the same or better similarities than models trained with . Although both losses are pixel-wise losses, the choice between and have a significant impact on the quality of our predicted videos.
We consider the motion and content decomposed GAN (MoCoGAN) model  as a representative unconditional GAN method from prior work, and use it to generate videos from the BAIR robot pushing dataset. We use their publicly available code and show qualitative results in Fig. 11. The results show the variant that uses patch-based discriminators, since this one achieved higher realism than the variant that uses image-based discriminators. Since this prior work demonstrates competitive results in comparison to other prior unconditional GAN methods, we chose it as the most representative recent example of purely GAN-based video generation for this comparison. MoCoGAN produces impressive results on various applications related to human action, which are focused on a single actor in the middle of the frame. However, it struggles on videos in the robot pushing domain where multiple entities are moving at a time, i.e. the robot arm and the objects it interacts with.
We use the same dataset as the one in the main paper, except that we use the robot actions. Each action is a 4-dimensional vector corresponding to Cartesian translations and a value indicating if the gripper has been closed or opened. As in the action-free dataset, we condition on the first 2 frames of the sequence and train to predict the next 10 frames. In this dataset, the video prediction model is now also conditioned on a sequence of actions , in addition to the initial frames. The generator network is modified to take an action at each time step, by concatenating the action to the inputs of all the convolutional layers of the main network, similar to how the latent code is passed in (but without the additional fully-connected LSTM). We show the realism and diversity results in Fig. 12 and the accuracy results in Fig. 13. In addition to the methods compared in the action-free dataset, we also compare to SNA , an action-conditioned deterministic video prediction model. The results indicate that our VAE model significantly outperforms prior methods on the full-reference metrics, and that our models significantly outperforms the model by Babaeizadeh et al.  both in terms of diversity of predictions and realism.