DyMoDreamer: World Modeling with Dynamic Modulation

We thank the reviewer for the thoughtful and constructive feedback. Below we address each of the raised concerns in detail.

1. Results on the held-out-level benchmark

We agree that generalization to unseen levels is crucial for assessing model robustness. Our current evaluation benchmarks (Atari 100k, DMC, and Crafter) are aligned with prior work focusing on sample efficiency and reward-driven dynamics modeling. Notably, the Crafter benchmark shares important characteristics with Procgen, such as procedurally generated content, stochastic transitions, and distributional shifts across episodes. Crafter already introduces distributional shift through its procedurally generated world, in which agent-centric motion relative to a dynamic background challenges traditional frame-differencing approaches. DyMoDreamer's superior performance on Crafter (9.5% improvement over DreamerV3) offers preliminary evidence that our dynamic modulation generalizes beyond static backgrounds.

Moreover, conducting a full evaluation across Procgen benchmark with DreamerV3's settings (the hard difficulty setting and the unlimited level set) would require approximately 16 (games) $\times$ 16.1 (days per task) $\times$ 5 (seeds) = 1288 (A100 GPU days). Since reducing the evaluation checkpoint to shorter environment steps often results in underdeveloped policies to Procgen benchmark, we conducted additional experiments on the DeepMind Lab benchmark, which is an egocentric 3D game platform designed for RL and contains difficult tasks (e.g.,maze navigation and objects exploration). Considering that our main goal is to improve the sample efficiency of RL algorithms, we shorted the evaluation checkpoint at 10M environment steps (100M steps in the DreamerV3 paper) and focused on several representative tasks with relatively dense reward signals, which are more likely to exhibit performance improvements within 10M steps [1] to assess DyMoDreamer’s performance. To ensure the fairness and quality of our results, we also reproduced DreamerV3 results using the official code and configurations, the corresponding results are reported below. In response to concerns about out-of-distribution generalisation, we ensure that all evaluations are conducted with randomized environment seeds.

DyMoDreamer outperforms the reproduced DreamerV3 baseline on 4 out of 5 tasks, showcasing strong performance particularly in environments with localized motion-dependent rewards (e.g., Explore Goal Locations Small, Explore Object Rewards Many) and dynamic visual input (e.g., Rooms Watermaze). In contrast, Rooms Keys Doors Puzzle—which prioritizes long-horizon memory and discrete, symbolic planning over visual motion cues—favors DreamerV3, aligning with our analysis of environment suitability.

While the differential observations in DyMoDreamer may not perfectly isolate task-relevant entities, they significantly reduce decision-irrelevant background clutter (e.g., the sky background). This suppression enhances exploration efficiency by directing the agent’s attention toward regions more likely to yield reward. Furthermore, as we discussed in lines 95-98, differential observations are not merely a visual processing technique, they also serve as a direct embedding of temporal information into the model’s representation, enriching its capacity to reason over dynamic sequences. Collectively, these results indicate that DyMoDreamer’s dynamic modulation mechanism also provides robust and generalizable benefits in visually complex and moderately egocentric domains, though its advantage may diminish in settings dominated by abstract reasoning or delayed, non-perceptual dependencies.

[1] Beattie C, et al. DeepMind Lab. arXiv:1612.03801, 2016.

2. Modulation in photorealistic or cluttered environments

While our current experiments are conducted in controlled simulators, the architectural design of DyMoDreamer emphasizes temporal change detection rather than reliance on appearance or segmentation priors. This property lends itself naturally to generalization in photorealistic or cluttered scenes (e.g., the Rooms Watermaze task in DeepMind Lab). Our default differencing mechanism employs a binary mask with a fixed threshold to highlight DyMoDreamer's generality and compatibility with a wide range of differencing strategies. In practice, DyMoDreamer can be readily extended to incorporate more robust alternatives, such as logical differencing to mitigate flickering backgrounds and exponential moving average differencing to suppress noise, as detailed in Appendix I.5. More importantly, the architecture is fully compatible with advanced dynamic extractors, including optical flow and attention-based motion segmentation modules, enabling a flexible and extensible framework suitable for complex visual scenes.

3. Benefits of pixel differencing over latent differencing

Similar to most prior work on world models, we provide both intuitive reasoning and experimental evidence for pixel-space differencing in Section 2.3. Specifically, pixel differencing maintains spatial precision for small but critical features (e.g., 1-pixel objects in Pong) that may be lost in latent encoding due to compression. Moreover, our ablation studies in Appendix I.3 confirms that latent differencing ($\delta_t = z\_t − z\_{t−1}$) underperforms pixel-based modulation, particularly when small motions are not captured by $z\_t$ in the experimental tasks.

4. Aggregated ablation table

Thank you for pointing this out. First, we would like to clarify that, as discussed in lines 294–297, the four Atari tasks selected for ablation were chosen because they exhibit distinct dynamic characteristics (e.g., sparse motion, and small/large object dynamics). These settings are closely aligned with the design goals of DyMoDreamer and allow for efficient and targeted evaluation of each architectural component’s contribution to dynamic modulation, since conducting all ablation studies across 26 Atari tasks are resource-intensive and infeasible effort given our time and funding budget at present.

In the final version, we will include an aggregated ablation table summarizing the performance of different ablation studies across the four Atari games (Boxing, Pong, Krull, Road Runner). A preliminary version of the table is:

These results reinforce that the dynamic modulation mechanism is crucial for robust performance across diverse game types, and that simply appending difference images without architectural integration leads to suboptimal results (Appendix I).

5.Comparison with MFRL and search-based methods

Compared to model-free approaches, DyMoDreamer exhibits significantly higher sample efficiency and achieves substantially better performance on a number of Atari tasks (compared with BBF). This highlights the strength of world model–based reasoning in low-data regimes. Furthermore, unlike model-free methods that often require millions of environment interactions to converge, DyMoDreamer reaches competitive or superior performance within a constrained budget, showcasing its practical advantages in sample-limited settings. Search-based methods such as MuZero requires 8 TPUs for training per task, whereas our JAX implementation of DyMoDreamer achieves competitive performance with just 1 GPU for 5.5 hours, demonstrating significantly better computational efficiency while maintaining the benefits of world model learning.

We hope that our responses have adequately addressed all your concerns. Please feel free to let us know if any further clarification is needed.

We sincerely thank you for the constructive feedback on our paper. Below, we address each concern raised, and all new experiments conducted in the response will be incorporated into the final version of our manuscript.

1. Generalization to egocentric environments DeepMind Lab

To evaluate DyMoDreamer's generalizability, we conducted additional experiments on the DeepMind Lab benchmark, which is an egocentric 3D game platform designed for RL and contains difficult tasks (e.g.,maze navigation and objects exploration). Classical methods (IMPALA and R2D2+) typically require over 1B environment steps to achieve non-trivial reward performance. Since our main goal is to improve the sample efficiency of RL algorithms, we shorted the evaluation checkpoint at 10M environment steps (100M steps in the DreamerV3 paper) and focused on several representative tasks with relatively dense reward signals, which are more likely to exhibit performance improvements within 10M steps [1] to assess DyMoDreamer’s performance. To ensure the fairness and quality of our results, we also reproduced DreamerV3 results using the official code and configurations, the corresponding results are reported below.

DyMoDreamer outperforms the reproduced DreamerV3 baseline on 4 out of 5 tasks, showcasing strong performance particularly in environments with localized motion-dependent rewards (e.g., Explore Goal Locations Small, Explore Object Rewards Many) and dynamic visual input (e.g., Rooms Watermaze). In contrast, Rooms Keys Doors Puzzle—which prioritizes long-horizon memory and discrete, symbolic planning over visual motion cues—favors DreamerV3, aligning with our analysis of environment suitability.

While the differential observations in DyMoDreamer may not perfectly isolate task-relevant entities, they significantly reduce decision-irrelevant background clutter (e.g., the sky background). This suppression enhances exploration efficiency by directing the agent’s attention toward regions more likely to yield reward. Furthermore, as we discussed in line 95-98, differential observations are not merely a visual processing technique, they also serve as a direct embedding of temporal information into the model’s representation, enriching its capacity to reason over dynamic sequences. Collectively, these results indicate that DyMoDreamer’s dynamic modulation mechanism also provides robust and generalizable benefits in visually complex and moderately egocentric domains, though its advantage may diminish in settings dominated by abstract reasoning or delayed, non-perceptual dependencies.

[1] Beattie C, et al. DeepMind Lab[J]. arXiv:1612.03801, 2016.

2. Robustness in noisy or dynamic background

Our default differencing mechanism employs a binary mask with a fixed threshold to highlight DyMoDreamer's generality and compatibility with a wide range of differencing strategies. In practice, DyMoDreamer can be readily extended to incorporate more robust alternatives, such as logical differencing to mitigate flickering backgrounds and exponential moving average differencing to suppress noise, as detailed in Appendix I.5. More importantly, the architecture is fully compatible with advanced dynamic extractors, including optical flow and attention-based motion segmentation modules, enabling a flexible and extensible framework suitable for complex visual scenes. Furthermore, our experiments in DeepMind Lab demonstrate that foreground object motion often conveys egocentric relative dynamics, which can be informative and beneficial for downstream policy learning.

3. Dynamical modulation and agent actions

We thank the reviewer for the thoughtful suggestion to condition the dynamic modulation mechanism on the agent’s actions. We agree that this is a promising direction, and in fact, we believe that the current version of DyMoDreamer already implicitly incorporates this idea. As our model is trained end-to-end, the dynamic modulators participate in the temporal inference process ($f\_{\phi}$ in Equation (3)) alongside the agent’s action, contributing to the prediction of future latent states. The world model is optimized jointly via a reconstruction and policy loss on fixed replay sequences, which inherently couples the modulation signal with the action trajectory. While we do not explicitly encode the action $a\_t$ into the computation of $d\_t$ , the action influences the next latent state $h\_t$, which in turn affects the encoding and interpretation of subsequent modulators $d\_t$, since the encoding process of $d_t$ is $d_t \sim q_\phi\left(d_t \mid h_t, o'_t\right)$. Thus, DyMoDreamer performs implicit action-conditioned modulation through temporal feedback in the recurrent dynamics model. We provide supporting empirical evidence for this interaction in Appendix H, although we did not explicitly constrain $d_t$ to focus on the part controlled by the agent, it naturally focuses more on agent-controllable dynamics (despite being decoded from all dynamic components).

4. Partial vs full dynamics-static disentanglement

We intentionally avoid explicitly separating dynamic and static components using hard static masking $(1-M(o\_t) \cdot o\_t)$ for the following reasons.

First, our differential observations are derived from frame-differencing followed by dilated convolutions, but not from sophisticated edge-aware segmentation techniques. As a result, the resulting dynamic masks $M(o\_t)$ highlight motion-correlated regions rather than clearly delineated object boundaries. The edges of these masks may not align with semantic object contours, and emphasizing such boundaries through hard segmentation may overemphasize potentially irrelevant edge pixels while neglecting the truly decision-relevant patterns within the masked regions $M(o\_t) \cdot o\_t$.

Moreover, since the differenced observation includes not only the changed pixels but also their local neighborhoods (as we metioned in lines 131-134), directly enforcing a binary split could disrupt the integrity of reward-relevant static features. For instance, partial inclusion of an important static object across both streams could prevent either $z\_t$ or $d\_t$ from capturing it in full, ultimately degrading decision quality. Our joint encoding approach circumvents this issue by allowing the model to learn a soft, task-driven decomposition guided by reconstruction and policy optimization signals.

5. Quantitative evaluation of dynamic feature modeling

Standard RL benchmarks typically lack precise real-time annotations, and more complex environments such as DMLab introduce additional visual challenges including stage-wise transitions and shifting viewpoints. As a result, there are no established segmentation or tracking metrics readily applicable for evaluating dynamics modeling within RL settings. In this work, we rely on task performance, imagination accuracy, and qualitative visualizations (Fig. 3, Appendix F) to assess the model's capacity for dynamic feature modeling. We believe these provide sufficiently comprehensive and task-relevant evidence in the absence of standardized evaluation protocols.

6. Grammatical errors and typos

We gratefully thank you for the careful check on our manuscript, and we will revise the manuscript accordingly:

$\bullet$ Line 130: In fact, very few pixels may exceed the threshold $\epsilon$ after being processed by $D(\cdot)$.

$\bullet$ Line 667: This emergent specialization suggests an natural segregation within the model’s representational architecture like the denoised Markov decision process [59], since we do not explicitly assign reconstruction targets to different decoders.

We hope we have addressed all your raised points. If there are anything unclear, we would be happy to provide further clarifications.

We sincerely thank the reviewer for their thoughtful feedback and follow-up question. To further clarify our design choices, we elaborate below on the motivation behind our current experimental setup and provide additional details regarding the average mask rate.

Regarding the 10M-steps comparison with DreamerV3

We appreciate the concern that DyMoDreamer and DreamerV3's performance on DMLab may continue to improve beyond 10M steps. However, we would like to respectfully point out that the original DreamerV3 paper itself does not always choose fully converged tasks, especially in complex benchmarks such as DMLab. In fact, experiments in DreamerV3 are also conducted under fixed step budgets (e.g., 100M for DM Lab), rather than until absolute convergence. Our evaluation protocol closely follows this precedent.

Importantly, DreamerV3 and DyMoDreamer are specifically designed to enhance sample efficiency, thus the performance in the early training phase is a central metric of interest. Moreover, the successful results of DyMoDreamer on DMLab under the 10M-steps setting demonstrate that our dynamic modulation mechanism generalizes well not only to allocentric control tasks, but also to egocentric visual environments such as DMLab. This is also the motivation behind our inclusion of the additional DMLab experiments and the cross-paradigm applicability suggests that the learned dynamics-aware attention is not limited to one particular observation structure, but can flexibly adapt to different types of visual input. Our experiments demonstrate that DyMoDreamer exhibits a significantly faster learning curve compared to DreamerV3 under the same 10M-step budget. Importantly, the slope of DyMoDreamer‘s curve beyond 8M steps remains comparable to DreamerV3, suggesting that the performance advantage is unlikely to vanish in the later stage. As we consider the practical constraints on training time and compute resources (since conducting a full evaluation across DM Lab benchmark would require approximately 30 (tasks) $\times$ 2.9 (days per task) $\times$ 5 (seeds) = 435 (A100 GPU days), we believe that evaluating DyMoDreamer under the 10M interactions constraint is both meaningful and justified since faster convergence is itself a valuable property for world models. This evaluation strategy aligns with the growing trend in the literature where many works (e.g. STORM [1], TWM [2], and MWM [3]) choose Atari100k or Meta-world with limited interactions as the sole benchmark to emphasize early-stage learning performance.

[1] Zhang W, et al. Storm: Efficient stochastic transformer based world models for reinforcement learning[J]. Advances in Neural Information Processing Systems, 2023, 36: 27147-27166.

[2] Robine J, et al. Transformer-based World Models Are Happy With 100k Interactions[C]. The Eleventh International Conference on Learning Representations.

[3] Seo Y, Hafner D, et al. Masked world models for visual control[C]. International Conference on Robot Learning. PMLR, 2023: 1332-1344.

Regarding the average mask rate

We have now included the average mask activation rates for the DMLab experiments, as shown in the table below. We would like to emphasize that the value of the mask rate does not directly determine performance. Rather, the mask serves as a mechanism to highlight regions of dynamic change, allowing the model to modulate its representation accordingly. Even relatively sparse masks (e.g., the Bank Heist task in Atari) can lead to meaningful improvements, as they focus learning on temporally salient features without introducing excessive noise. Our empirical results indicate that performance gains are more influenced by the effectiveness of the modulation than the density of the mask itself.

We hope this response clarifies the rationale behind our evaluation protocol, and we sincerely appreciate your time and consideration in reviewing our additional clarifications.

To further address the reviewer’s concern, we have extended the experiments to 25M environment steps as of the time of this comment. Preliminary evaluations indicate that DyMoDreamer continues to maintain its earlier advantage (we proposed in the rebuttal) over DreamerV3. Notably, DyMoDreamer has already surpassed DreamerV3’s performance in the Rooms Watermaze environment at a converged level, and the corresponding results are reported in the table below. We are continuing to run the experiments to 100M steps and will include these results in the final version of the paper, which we expect will further substantiate DyMoDreamer’s ability to handle allocentric environments while preserving strong sample efficiency.

We sincerely thank the reviewer for the insightful comments. Below, we address each point in detail, and we will incorporate clarifications and additional results in the final version.

1. Dimensionality of stochastic representations $z\_t$

We analyzed the effect of dynamic modulators' dimensionality in Appendix I.5, and additionally examined how the dimensionality of the original stochastic representations $z\_t$ influences overall performance. The results are summarized in the table below. Our findings indicate that a low-dimensional $z\_t$ also leads to degraded performance. As we discussed in Appendix H, $z\_t$ does not merely encode static content. Visualization suggests that $z\_t$ tends to capture dynamic elements in the environment that are beyond the agent’s control, whereas the dynamic modulators $d\_t$ focuses more on agent-controllable dynamics (despite being decoded from all dynamic components). Therefore, reducing the dimensionality of $z\_t$ limits the model’s capacity to capture rich environmental dynamics, leading to a notable drop in overall performance. This is why we don't use a completely static fixed $z$. In fact, in our early experiments, we have explored a variant where a fixed static vector $z$ replaced $z\_t$ to encode/decode only the background (achieved by averaging over the batch length dimension), while only the dynamic modulators $d\_t$ were used to drive the sequence model. Under this configuration, the performance was comparable to or worse than vanilla DreamerV3, as the static background can shift over the course of an episode (e.g., the level transitions in Krull). A fully fixed $z$ lacks the flexibility to adapt to such stage-wise changes in the static background, ultimately hindering representation quality and decision-making.

2. Clarification on the “Removing Dynamic Modulation”

In this ablation, a single decoder is used to reconstruct only the original observation $o\_t$, without reconstructing the differential observations $o'\_t$. The decoder receives a concatenation of $z\_t$ (encoded from $o\_t$) and $d\_t$ (encoded from $o'\_t$) as input, which is fed through a shared decoding head (the reconstruction process is formulated the same as Equation (1)). In this configuration, $d\_t$ is not explicitly embedded into the RSSM as in our dynamic modulation design.

3. Baseline with $\mathcal{L}\_{reg}$

We thank the reviewer for this insightful comment. In response, we implemented a baseline using DreamerV3 with the same divergence regularization term $\mathcal{L}\_{reg}$ as DyMoDreamer but without dynamic modulation. This variant showed minor improvement over DreamerV3 but underperformed compared to DyMoDreamer (in the following table). The results demonstrate that the differential divergence regularization acts as a complementary supervisory signal that works in concert with reconstruction objectives, and contributes improvement through its unique ability to constrain the temporal consistency in the reconstruction process of vanilla DreamerV3.

4. Applicability beyond images and generality to other world models

To evaluate the applicability of DyMoDreamer in state-based environments, we conducted experiments on DeepMind Proprio—a proprioceptive control benchmark where observations consist of structured state vectors such as velocity and position. In this setting, observation differencing naturally reduces to state differencing, with temporal dynamics being more explicitly encoded. Consequently, differential modulation provides similar benefits in non-visual settings, since such differences also carry meaningful physical semantics similar to the differential observations—for instance, differential positions implicitly encode velocity, while the differential velocities reflect acceleration.

To further validate the effectiveness of our dynamic modulation mechanism, we integrated it into STORM [1], a recent efficient transformer-based world model. As shown in the results below, this integration also leads to clear performance gain.

[1] Zhang W, et al. STORM: Efficient stochastic transformer based world models for reinforcement learning. Advances in Neural Information Processing Systems, 2023, 36: 27147-27166.

5. Broader impact of architectural biases

A naive separation of dynamic and static components may introduce inductive biases in certain environments. To mitigate such issues (dynamic backgrounds or environmental noise), we provide several alternative differencing strategies in Appendix G, including multi-frame logical differencing and moving average differencing. Importantly, the dynamic modulation mechanism is highly compatible with a wide range of advanced, difference-based computer vision techniques. This extensibility suggests that DyMoDreamer possesses strong generalization potential, as differencing is a foundational principle in many visual detection methods.

6. Discussion of modulated ODEs and latent flow

While modulated ODEs also employ modulation operators to enhance the temporal modeling in neural ODEs, our approach differs in several key aspects. In modulated ODEs, modulators are time-invariant and trained as a global statistic across the entire sequence, whereas DyMoDreamer extracts modulation explicitly from differential observations at each timestep. Additionally, modulated ODEs encode modulators from the full input sequence rather than isolating dynamic cues via differential observations. As a result, modulated ODEs are primarily suited for modeling passive, uncontrolled dynamics, whereas our dynamic modulation framework enables explicit modeling of environment transitions conditioned on agent actions.

The latent flow methods largely focused on model-free reinforcement learning and do not introduce dedicated encoders or decoders for the latent flow $\delta\_t$. The latent flow $\delta\_t$ are not designed to be predictive but serve as auxiliary information injected into decision-making. In contrast, DyMoDreamer explicitly incorporates the dynamic modulators into the reconstruction process to mitigate hallucinations in dynamic regions (as shown in Fig. 3). Moreover, the modulators $d\_t$ are fully predictive and plays a central role in improving the world model’s capacity to model temporally coherent dynamics.

7. Revision in the manuscript

We gratefully appreciate your valuable comments and suggestions, and we will revise the manuscript accordingly:

$\bullet$ We will clarify the distinction by rewriting the sentence in line 27 as: “A key approach to addressing this challenge is the general framework of world models, which learns compact latent dynamics for planning and decision-making. One early instantiation of this framework, proposed by Ha & Schmidhuber, combines a VAE with an RNN and uses evolutionary strategies to optimize policies in the learned latent space.”

$\bullet$ Equations (2) & (9): We will introduce the indices in natural language before the equations to improve clarity. Specifically, we will indicate the meaning of each index (e.g.,$i$ is the time dimension, $h$ and $w$ are spatial dimensions, and $c$ is the channel dimension) to assist readers unfamiliar with the notation.

We appreciate the reviewer’s thoughtful feedback and hope that our rebuttal has addressed your concerns. Please kindly let us know if further details are required.

We sincerely thank the reviewer for the comprehensive evaluation and respond to the raised concerns below, specifically regarding the generalizability of DyMoDreamer to egocentric domains, the rationale behind the latent-difference ablation design, and the necessity of discussing explicit object dynamics or 3D modeling approaches. All additional experiments referenced in this rebuttal will be included in the final version of the paper.

1. Evaluation on egocentric DM Lab tasks

In response to the concerns about the evaluation on more explicitly egocentric environments, we conducted additional experiments on the DeepMind Lab benchmark to further validate DyMoDreamer's effectiveness under rapid viewpoint changes. To the best of our knowledge, among existing world model literature, only DreamerV3 has been evaluated on this benchmark. Unfortunately, we were unable to locate a readily integrable pip package or a pre-configured Dockerfile for streamlined deployment, therefore setting up the environment and managing dependencies via Bazel incurred substantial overhead during our supplementary experimentation phase. Moreover, conducting a full evaluation across DM Lab benchmark would require approximately 30 (tasks) $\times$ 2.9 (days per task) $\times$ 5 (seeds) = 435 (A100 GPU days). To make the evaluation tractable, we shorted the evaluation checkpoint at 10M environment steps (100M steps in the DreamerV3 paper) and focused on several representative tasks with relatively dense reward signals, which are more likely to exhibit performance improvements within 10M steps [1] to assess DyMoDreamer’s performance. To ensure the fairness and quality of our results, we also reproduced DreamerV3 results using the official code and configurations, the corresponding results are reported below.

DyMoDreamer outperforms the baseline on 4 out of 5 tasks, demonstrating competitive performance particularly on tasks with localized motion rewards (e.g., Explore Goal Locations Small, Explore Object Rewards Many) and dynamic visual input (e.g., Rooms Watermaze). However, in Rooms Keys Doors Puzzle, which emphasizes long-horizon memory and discrete planning over motion cues, DreamerV3 shows a slight advantage, consistent with our analysis of task suitability. In such settings, although the differential observations may not isolate only the task-relevant objects, they nonetheless effectively suppress large portions of decision-irrelevant background. This facilitates more efficient exploration by directing the agent’s attention toward reward-associated regions of the scene. Furthermore, as we discussed in lines 95-98, differential observations are not merely a visual processing technique, they also serve as an embedding of temporal information into the model’s representation, enriching its capacity to reason over dynamic sequences. These results suggest that DyMoDreamer’s dynamic modulation mechanism offers generalizable benefits in visually rich and moderately egocentric environments, though it may be less effective in domains requiring complex, abstract reasoning or long-term symbolic memory.

[1] Beattie C, et al. DeepMind Lab. arXiv:1612.03801, 2016.

2. Latent-difference ablation design

We thank the reviewer for the valuable remark. Our initial choice, directly subtracting latent states to construct $\delta_t=z_t-z_{t-1}$ without re-encoding or spatial structuring was intentional to establish a conservative baseline for comparison with DyMoDreamer. To ensure a more rigorous and fair ablation, we conducted an additional ablation experiment where $\delta_t$ was not only fed into the sequence model ($h\_t = f\_{\phi}(h\_{t-1}, z\_{t-1}, \delta\_{t-1}, a\_{t-1})$), but also participated in the reconstruction ($p\_{\phi}(\hat{o\_t}|h\_t,z\_t,\delta\_{t})$, $p\_{\phi}(\hat{r\_t}|h\_t,z\_t,\delta\_{t})$, and $p\_{\phi}(\hat{c\_t}|h\_t,z\_t,\delta\_{t})$) and the policy learning processes ($s\_t= \lbrace h\_t,z\_t,\delta\_{t}\rbrace$). In this configuration, the usage of the latent flow $\delta_t$ aligns with its formulation in the original work, except that it additionally participates in the reconstruction process. As reported in the table below, substituting $d\_t$ with $\delta\_t$ does not lead to improved performance, further underscoring the unique effectiveness of our proposed dynamic modulation signal. As discussed in Section 2.3 (lines 187–194) and Appendix I.3, we empirically confirmed that differencing in latent space will fail to capture subtle but critical motion signals (e.g., 1-pixel ball in Pong) due to quantization and precision loss, ultimately leading to degraded performance.

3. Discussion on modeling object dynamics

Explicitly modeling object dynamics using 3D priors or physics engines is an important direction. Our work emphasizes an orthogonal strategy: enhancing dynamic feature capture without explicit object segmentation or prior assumptions will improve the world model's performance. To more explicitly explore the incorporation of object dynamics through prior modeling, we conducted an additional experiment in which the differenced observations were replaced with a pretrained computer vision module "Cutie". Cutie, informed by prior knowledge, is capable of directly extracting key objects from the scene after pretraining. In this setting, the dynamics captured by $d\_t$ (where $d\_t$ are encoded from the Cutie's output in this case) corresponds exclusively to the motion of key objects, with other information effectively excluded. While this approach does yield performance gains comparable to those of DyMoDreamer, it introduces additional training overhead through reliance on supervised pretraining, and incurs a higher computational cost than our lightweight modulation mechanism.The results of this experiment are presented below.

We hope our response has resolved the concerns, and please let us know if any additional clarifications are required.