Venue: ICLR 2023 Conference

Reviews:

final_score: rating: 3: reject, not good enough
review_content: summary_of_the_paper: This paper proposes a method called Action Matching for learning generative models. In particular, this technique falls along the lines of score-based / diffusion probabilistic models, by learning about the 'derivative' of the probability distribution rather than directly modeling the density.

The paper claims that the main difference between action matching and score matching is that action matching learns about the derivative along the time axis. The argument is that a distribution can be complicated to model for each time slice, but actually has very little change w.r.t. time, so modeling this change w.r.t. time can make the learning problem easier.
strength_and_weaknesses: I don't think the method proposed in this paper is new.
It seems to be the same as the idea of learning "time scores", e.g., change in distribution through time.
https://arxiv.org/pdf/2111.11010.pdf

Furthermore, the paper claims that Action Matching can be preferred over score matching since score matching can only handle the forward process of noising, and not of more general transformations like decolorization. I don't think this is true, e.g., this paper below.
Their experimental results are much better than the ones presented here.
https://arxiv.org/pdf/2201.11793.pdf
clarity,_quality,_novelty_and_reproducibility: I did not enjoy the writing in this paper. There is a lot of meandering and discussion that is neither rigorous nor relevant to the target audience of this conference. E.g.
"For example, in Quantum Mechanics, the act of measurement at a given point collapses the wave function which prevents us from obtaining further samples along that trajectory." is a particularly egregious example, but others throughout.

The most important parts of training procedure and loss are glossed over and presented in a roundabout way, which is not at all clear (e.g., the "analogy with VI and generative modeling" paragraph was very hand-wavy not a good use of space.).

The citations section is also way too sparse.
summary_of_the_review: The paper proposes Action Matching to learn the change in distribution through time. The paper claims that Action Matching can handle more general forward processes (decolorization, masking...). 

However, it appears that the idea of learning "time scores" is not new, and previous diffusion based methods can already handle these more general forward processes. Furthermore, the writing is not clear and concise, and the experimental results are weak.
review_title: null

final_score: rating: 6: marginally above the acceptance threshold
review_content: summary_of_the_paper: In this paper, the authors show that many continuous dynamics can be represented as a continuous vector field and propose a method called action matching that can learn the vector field. One key idea is that instead of learning the distributions themselves, the method aims to learn only the dynamics. This can be effective when dynamics are simple but distributions are complex. On multiple image generation tasks, the method outperforms score matching by a clear margin.



strength_and_weaknesses: Strengths:
+ The proposed method is theoretically sound and general. It can potentially have a wide range of impact beyond image generation.
+ Multiple vision tasks are evaluated, including diffusion, colorization, and impainting. Furthermore, results show consistent improvement on multiple image datasets. I find the results convincing.

Weaknesses:
- While the proposed method is general, the experiments are limited to low-resolution image generation tasks. Experiments on tasks beyond image generation (e.g. natural sciences ones), even just toy examples, can be interesting.

clarity,_quality,_novelty_and_reproducibility: The writing is clear and easy to follow. The idea is novel and original.
summary_of_the_review: Overall the study presented in the paper is sound and promising. Both the theoretical and empirical results are convincing.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: This paper an action matching method to learn broader family of stochastic dynamics. Instead of modeling the distributions at each time-step, the action matching directly learns an underlying mechanism to move samples in time. Experimental results show that the proposed method can be applied to image super-resolution, colorization, and so on. 

strength_and_weaknesses: Strength: 

Using action matching to avoid modeling the distributions at each time-step is interesting. Experimental results are able to demonstrate the effect of the proposed method.

Weaknesses: 

Action matching is based on the diffusion model. However, it is not clear whether the proposed action matching performs better or not. 

In addition, it lacks comparisons the with the related methods. Only showing the results of the proposed method is not enough. 

It is not clear whether the proposed action matching has a better convergence property or not. 
clarity,_quality,_novelty_and_reproducibility: The paper is well written. However, based on the descriptions of the paper, reproducing the results is not trivial. 
summary_of_the_review: Lacking analysis and comparisons with the related methods.
review_title: null

final_score: rating: 5: marginally below the acceptance threshold
review_content: summary_of_the_paper: The authors proposed a method that enables us to learn a broader family of stochastic dynamics by directly learning an underlying mechanism to move samples in time without modeling the distributions at each time-step. The contributions are as follows:

1. Action Matching relies only on samples and does not require any knowledge of the underlying stochastic dynamics by learning only the dynamics, which is based on a mathematically well-defined formulation and useful when a complicated distribution has simple dynamics. 
2. They discussed Action Matching as a variational framework for learning these dynamics
3. For applications of Action Matching, they performed computer vision tasks with several stochastic equations such as generative modeling, super-resolution, colorization, and inpainting. 


strength_and_weaknesses: Strength: 
* The idea of the above first contribution is interesting and may have a novelty.
* The experimental results clearly show the superiority of the proposed approach.

Weakness:
* The presentations (in particular the first half of the main text) and figures were unclear to me, which is described as the specific comments.
* It may be a small weakness: in my understanding, the generative model of the proposed approach needs the definition of dynamics, but the previous action-matching methods also require it. 

Specific comments
* In the Introduction, q_t and “score matching” were not defined and then Fig. 1 was meaningless.
* In my understanding, this method can apply to the dynamics which can be expressed as curl free vector fields. Is this correct? Are there any other dynamics than you analyzed? 
* Fig. 3: what are the two types of pictures for Score/Action matching?
* Fig. 4: If they are generated, the information of input and the dynamics may be necessary for understanding. Moreover, MINST was not used in the main text.
* FID may be not defined.

clarity,_quality,_novelty_and_reproducibility: The presentation was clear in total but I found the above unclear points. The quality may be good in total because of the above contributions and strengths. The experiments may not be reproduced because they did not provide the code.

summary_of_the_review: Based on the comment above, I consider that the weakness of this paper outperformed the strength at this stage, then I cannot give a higher rating.
review_title: null

Meta-review: metareview:_summary,_strengths_and_weaknesses: This paper proposes a method they name Action Matching for modeling stochastic dynamics of generative models. This technique falls along the lines of score-based / diffusion probabilistic models, by learning about the 'derivative' of the probability distribution rather than directly modeling the density.

The reviewers were unanimous in rejecting the paper (the average score of 4.75 is clearly below the acceptance bar). Despite some of the reviews having some incorrect statements (as pointed out by the authors), there are two important points that were raised to which I largely agree: 1) a lack of discussion regarding the overlap with prior work and 2) limited experimental results (which is an important aspect as the paper is more empirical). The reviewers did not change their opinion during the discussion period (although I note that not all reviewers participated in the discussion). 

Overall, I think there are some important problems to be fixed and I am therefore not able to recommend acceptance at this time.
justification_for_why_not_higher_score: This is clearly a rejection from my point of view. I did try to initiate a discussion with the reviewers and sent several emails to them but there was no response. Based on my own reading of the paper and the reviews, I find that two aspects are clearly lacking: discussion of the overlap with prior work and limited experimental results (which I believe is an important aspect as the paper is more on the empirical side).
Decision: Reject