DiverseFlow: Sample-Efficient Diverse Mode Coverage in Flows

• Section 6.4 uses abbreviations like CFM, SB-CFM, and OT-CFM without defining them right away, which leaves readers guessing. Clear definitions upon first mention would help make the section easier to follow.
• The image generation results mostly rely on displaying images to demonstrate diversity, with only a few qualitative measures tucked away in the appendix.
• The method's complexity—specifically, the cost of calculating gradients of eigenvalues at $O(k^3)$—could potentially be reduced to $O(k^2)$ with some algorithms, but it is still significant. This makes it hard to scale to larger values of sampling points $k$. For smaller values of $k$ (like $k=2$ to $10$, as mentioned in the paper), simply sampling multiple times independently could offer similar diversity without requiring much computation. Given recent advances in diffusion sampling techniques, normal sampling is not a significant issue.
• Adding extra terms to the sampling process can often make samples diverge from stable paths, which might be why the method still requires a high number of sampling steps (up to 100) to stabilize the sampling. This supports my previous point that it might be better to use accelerated sampling techniques and sample more points. The paper does address this.

• Although the method is theoretically sound, its performance and evaluation remain questionable. Need to provide more quantitative metrics like precision & recall [1].
• I’m curious whether using variance as a simple gradient function is still effective. Since the core idea of Determinantal Point Processes (DPP) is to promote diversity in generated samples through the feature space of a pretrained model, variance could also serve as a useful indicator for this purpose. This can be considered as a simple baseline to compare with.
• DPP bears some similarities with PCA (principle component analysis), particularly in choosing the most K principle eigen components to better represent the original space. The authors should expand on this comparison.
• Is the imposed gradient constraint applicable during the training phase? Because the method is inadvertently limited to the coverage modes of pretrained model.
• Figure 5, using DiverseFlow seems to increase the contrast and make the color saturated. Why is that?
• The guidance scale in CFG sampling is known to negatively impact the diversity of generated examples. In figure 5, the method used a scale of 8 which is really large. Why do the authors not use a lower scale like under 3.0 for experiments? The gain of method is really marginal in this experiment.
• Honestly, the improvements shown in qualitative Figures 3, 4, 5, and 8 are not very convincing, as the differences are minimal in some cases.

Paper exposition should be improved:

• The captions of figure 2 have rendering issues. Should add notation of green dots in the figure for clarity.
• The notation of source and target distribution are unclear as in figure 2a.
• How $\gamma_t$ is constructed?

Ref: [1] Kynkäänniemi, Tuomas, et al. "Improved precision and recall metric for assessing generative models." Advances in neural information processing systems 32 (2019).

• while the theory seems compelling to me, the visual results seems to have a few issues, which should be mentioned and discussed in the paper: firstly, quality of sampled Diverseflow images seem to be worse - e.g. in Fig3(b lower image) the boxer seems to merge with the rope, or in Fig3(d) the lower white crane has a very unrealistic neck. Secondly, while the model adds diversity, it seems to also mix concepts for polysemous prompts: "a famous boxer" shows an image with a boxer (sports) and also a dog in the same image instead of either. Same for the mechanical crane, which has a shape akin to the animal, and also for the deer buck coin. Also, while Fig4 shows some changes even in identity (4c), the added diversity in Fig4e is very subtle to notice.
• In section 6.3. it is claimed that the model "maintain(s) the high quality of the samples and simultaneously explore more modes in the dataset." and then references Fig5. However, the diversity samples without CFG is arguably largest. This raises the question if there is maybe a CFG strength that leads to both diverse and high-quality samples. A plot that shows this front with varying CFG strength (e.g. Aesthetic score or FID on one axis, and diversity on the other) and demonstrating that the model really is outside this front, would put more compelling evidence behind the statement.
• a Limitation section is missing. Clearly the model has limitations. E.g. it would be important to discuss that the model needs more memory (when naively implemented at least), as the coupling between ODEs implies the need to keep all generations in memory simultaneously.
• the statement "observe that though DiverseFlow obtains better diversity at similar quality, the aesthetic score of Particle Guidance is quite low, suggesting poor quality." should be made more clear. I.e. it's a bit unclear what 'better' refers to (presumably the IID model), and it should be pointed out that according to the plot PG has higher diversity, but this comes at the cost of lower aesthetic score. To make a more direct comparative statement between PG & DF it'd be great to push PG to higher aesthetic scores, or DF to more diversity (such that they have common aesthetic score values).
• a bit more minor: ideally, add more trials in Figure 9b, such that DiverseFlow is not at 10, but rather 9.96 or something, to allow some future comparisons.

1. Authors would have shown how DiverseFlow would work for non-polysemous prompts, and/or for sentence-wide prompts "A boxer is running on a trail" vs "A boxer"?
2. Authors have shown the diversity through 4x4 grid however it will be informative to know the diversity proportion in the sampling budget. experiment concerning sampling budget
3. Could you add how other generative models behave in the absence of such a diverse sampling scope?
4. Re-check the 6.5 section for the quoted results in bold. Maybe, check all other sections too for any missing equations or typos.