We propose an approach for sequence modeling based on autoregressive normalizing flows. Each autoregressive transform, acting across time, serves as a moving reference frame for modeling higher-level dynamics. This technique provides a simple, general-purpose method for improving sequence modeling, with connections to existing and classical techniques. We demonstrate the proposed approach both with standalone models, as well as a part of larger sequential latent variable models. Results are presented on three benchmark video datasets, where flowbased dynamics improve log-likelihood performance over baseline models.
Summary 
The paper proposes to combine the video modeling approaches based on autoregressive flows (e.g. Kumar’19) with amortized variational inference (e.g. Denton’18), wherein an autoregressive latent variable model optimized with variational inference is extended with an autoregressive flow that further transforms the output of the latent variable model while allowing to compute exact conditional probability. This is motivated with a physical intuition, where a dynamics model can benefit from decorrelating the inputs, and it is demonstrated that layers of autoregressive flows can represent derivatives of the original signal. In a proof-of-concept experiment, it is shown that using a layer of autoregressive flow improves NLL of a latent variable model.
Decision
The paper presents an interesting method and tackles an important problem. At the same time, the properties of the proposed method are not well exposed and the experimental evaluation is incomplete. Moreover, the motivation of the paper is confusingly disconnected from the proposed model. I rate this paper as borderline, but am hopeful that some of the issues will be clarified during the discussion period.
Pros
- The paper is well-motivated and tackles a significant problem.
- The proposed method is novel.
- The paper is well-written.
Cons
- The experimental evaluation is incomplete and does not expose the properties of the method fully. Comparisons to prior art are missing. (see below)
- The motivation is disconnected from the proposed model. The introduction of the paper motivates a model that hierarchically decorrelates a sequence of frames to arrive at a fully factorized model, which is later motivated with a physical example. However, the method proposed in the paper is instead a single layer of autoregressive flow on top of a powerful latent variable model! This is expressed in the title, but only glossed over in the abstract and introduction. The writing has to be updated to coherently focus on the contribution of the paper. 
Questions (ordered by decreasing importance)
1. In table 1, quantitative results are reported for the introduced methods. It is shown that introducing autoregressive flows achieves better likelihood and better generalization. However, quantitative comparisons with published methods that were evaluated on these datasets are missing, such as Denton’18 and Kumar’19. A quick calculation shows that Kumar et al. achieves a log-likelihood of -0.43 in Table 1 when converted to this paper’s metric, although it is possible my conversion is incorrect. Is the presented model competitive with previously published results? 
2. No qualitative generation results are presented. Since the model achieves a high likelihood it is likely to do well on one-frame prediction, and possibly would even work on autoregressive multi-step prediction. Is the model capable of generation of diverse and plausible video?
3. The paper has a lengthy section 3.1 that convincingly explains that decorrelating latent variables in time is important for sequence modeling. However the proposed approach in fact produces latents that are correlated in time! Since the prior over latent variables is conditioned on past frames, the model can in fact learn a correlated representation and still achieve optimal likelihood. Moreover, the position of both the digit and the robot arm could be seen in what should be the decorrelated image in Fig 4. Is there solid quantitative (or even qualitative) evidence that the model learns a ‘more decorrelated’ representation beyond the fact that it copies the background and that the likelihood improves? The evaluation in this paper does not convince me that the model learns a temporally decorrelated representation.
4. Were modern techniques beyond affine flows considered, such as from Kingma’18, Kumar’19? Two layers of affine flows are likely insufficient to model the complexity of these data, which makes the comparison to the purely flow-based models somewhat unfair.
5. It is stated that the paper is “the first to demonstrate flows across time steps for video data”, however, the related work by Kumar et al. proposes a somewhat similar model in which conditional flows are used to model video data. Do Kumar et al. not “demonstrate flows across time steps”?
Minor comments
1. Eq (10) and (12) seem to be inconsistent. Perhaps x_t = x_t-1 + u_t-1 was meant in eq (10)?
2. Line before eq(14): it not true that u_t-1 = x_t-1 - x_t-2. It would be true if the deterministic x_t = x_t-1 + u_t-1 model was assumed instead of the gaussian N(x_t; x_t-1 + u_t-1, Sigma). It is possible that eq(14) is still correct as the variance of Gaussians is additive.
3. The following work uses autoregressive flows for modeling temporal dynamics and should be cited: Rhinehart’18,19
Rhinehart et al, Deep Imitative Models for Flexible Inference, Planning, and Control
Rhinehart et al, PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settings
--------------------- Update 11.19 -----------------------
The newly provided experiments support some of the claims of the paper. In particular, I appreciate the plot showing that the proposed method successfully learns a more decorrelated representation over time, and the provided qualitative samples from the model. The authors also clarified my questions about motivation. At the same time, the proposed method is not shown to compare well to state-of-the-art approaches. I am leaning towards accepting the paper, but I believe the method would have a much larger impact if its properties were more fully exposed.
== comparison with Denton&Fergus'18 (SVG) ==
When trained with beta=1, as the authors suggest for comparison, this method is known to perform poorly. There are two possible ways of alleviating this: 1) to train with the modified objective as in the paper but evaluate the true lower bound on the likelihood, or 2) interpret the beta as the fixed variance of the decoder distribution. Given the results the authors have provided, I believe the latter option will lead to SVG outperforming the proposed approach.
== Correlation plot == 
Thanks for performing this experiment! While measuring correlation only captures linear dependencies, which is likely mostly the background image, this plot shows that the model indeed learns to (linearly) decorrelate the frames in the sequence. 
== Samples == 
Thanks for providing samples from the model! While the performance on BAIR is not quite convincing, the MNIST samples look very good.
= Kumar et al. comparison ==
The author's response convinces me that the proposed model is significantly different from Kumar et al. in scope, as Kumar et al simply use a per-frame normalizing flow encoder coupled with a sequential prior.
== eqs. 10, 12 ==
The authors' response cleared my confusion, the equations are correct.