Response to Reviewer HqJT
We thank Reviewer HqJT for the time and effort in reviewing our paper. Per your questions, please see our response below:
**1. Lack of novelty and idea coincides Kim et al.**
Before submission, we were aware of Kim et al.'s work [1]. However, we respectfully disagree regarding the similarity of their method to ours. While both methods are grounded in Stein's method, the underlying principles significantly differ. In their approach [1], the SVGD-based update takes the form of the Stein discrepancy: $\max_{\phi \in \mathcal{F}} \mathbb{E}\_{x\sim q(x)} [\phi(x) \nabla \log p(x) + \nabla \phi(x)]$, where $\phi(x)$ is often interpreted as an update direction constrained by a function class $\mathcal{F}$ (RBF RKHS in [1]). In contrast, our update rule appends a zero-mean random variable via the Stein identity after the raw gradient of the KL divergence: $\mathbb{E}_{x \sim q(x)} [\nabla \log p(x) + \phi(x) \nabla \log q(x) + \nabla \phi(x)]$, where $\phi(x)$ typically represents a pre-defined baseline function. The potential rationale behind [1]'s approach to reducing variance lies in introducing the RBF kernel as a prior to constrain the solution space by modeling pairwise relations between data samples. Our approach to reducing variance is centered around constructing a more general control variate that correlates with the random variable of interest, featuring zero mean but variance reduction. We have cited [1] and included the above discussion in our revised submission (Sec. 4.3).
[1] Kim et al., Collaborative Score Distillation for Consistent Visual Editing. NeurIPS 2023.
**2. Clarification on training steps and quantitative results.**
The qualitative results presented in this study were generated using a default setting of 25k training steps, consistent with the threestudio repo's default configuration. An error was identified in the original Fig. 7, where the x-axis required scaling to 25k due to our oversight in using the number of data points as the x-axis reference. We have rectified this error in the updated Fig. 7. To verify 25k is sufficient for convergence, we extended the training of ProlificDreamer by an additional 10k steps. During this extension, the CLIP score ranged between 0.74 and 0.75. Furthermore, a quantitative comparison is provided below.
| method | tulip | sushi car | lionfish |
|:--------------------|--------:|------------:|-----------:|
| DreamFusion | 0.777 | 0.862 | 0.751 |
| ProlificDreamer | 0.751 | 0.835 | 0.749 |
| SteinDreamer | 0.734 | 0.754 | 0.735 |
| method | cheesecake castle | dragon toy | michelangelo dog |
|:--------------------|--------------------:|-------------:|-------------------:|
| DreamFusion | 0.902 | 0.904 | 0.789 |
| ProlificDreamer | 0.843 | 0.852 | 0.775 |
| SteinDreamer | 0.794 | 0.806 | 0.769 |
The notably superior performance suggests that our method not only enhances quality at the early stages but also improves overall quality with full training.
**3. Correction on Janus results.**
We apologize for the inclusion of an incorrect video demo in the previous supplementary material, an oversight that occurred during the manuscript preparation rush. The updated supplementary material now accurately demonstrates that our method can potentially mitigate the Janus problem, although it is not the primary goal of this paper.
**4. The number of examples is limited.**
To enhance our experiment results, we present an additional set of four qualitative results on scene generation in Appendix C.4. As previously noted, our method consistently delivers smooth and visually consistent outcomes. Their video demos can be found in our updated supplementary materials.