We thank the reviewer for acknowledging this work contains exciting novel ideas with strong empirical results, and the general evaluation follows standard practice. And we appreciate the constructive feedback on the current manuscripts and we provide responses as follows:

Weakness 1: Missing variance estimate on model performance

We thank the reviewer for the suggestion and agree that providing variance estimation on metrics would enhance the interpretability of the results beyond the standard mean metrics. We repeated the inference for our model and baseline models five times with different random seeds. From which, we report the mean and standard deviations for each experiment as follows:

• Pearson correlations of conformation changes between sample and reference on multi-start (Table 1): | Type | Model | Traj. | Frame | ∆Frame | |----------|-----------|----------|----------|----------| | CA | MDGen | 0.56±0.03 | 0.47±0.03 | 0.41±0.02 | | CA | ConfRover | 0.75±0.01 | 0.63±0.01 | 0.53±0.01 | | PCA | MDGen | 0.18±0.01 | 0.15±0.01 | 0.10±0.01 | | PCA | ConfRover | 0.73±0.01 | 0.50±0.01 | 0.43±0.00 |

• State recovery in 100ns simulation (Table 2). MD reference does not contain repeats. | exp | Avg JS-Dist | Avg Recall | Avg F1 | |:----------|:--------------|:-------------|:----------| | MDref | 0.31 | 0.67 | 0.79 | | MDGen | 0.56±0.01 | 0.29±0.01 | 0.42±0.01 | | ConfRover | 0.51±0.01 | 0.42±0.00 | 0.58±0.00 |

• Pearson correlation on main dynamic mods between sample and reference trajectory. (Figure 5A shown as table.) MD reference does not contain repeats. | Components | Model | lag=1 | lag=5 | lag=10 | lag=20 | |------------------|----------------|--------------|-------------|------------|----------| | PC 1 | MD 100ns | 0.13 | 0.17 | 0.18 | 0.22 | | PC 1 | MDGen | 0.10±0.01 | 0.11±0.02 | 0.12±0.01 | 0.13±0.01 | | PC 1 | ConfRover | 0.16±0.02 | 0.18±0.01 | 0.19±0.01 | 0.20±0.01 | | PC 2 | MD 100ns | 0.17 | 0.16 | 0.18 | 0.18 | | PC 2 | MDGen | 0.11±0.01 | 0.11±0.01 | 0.11±0.01 | 0.12±0.01 | | PC 2 | ConfRover | 0.18±0.01 | 0.17±0.00 | 0.18±0.01 | 0.19±0.01 |

• Time-independent conformation sampling (Table 3). We were not able to get repeated results from AlphaFlow due to long inference time and limited resource. | exp | Pairwise RMSD r | Per target RMSF r | RMWD | MD PCA W2 | Joint PCA W2 | Weak contacts J | Transient contacts J | Exposed residue J | |:----------|:------------------|:--------------------|:----------|:------------|:---------------|:------------------|:-----------------------|:--------------------| | AlphaFlow | 0.53 | 0.85 | 2.64 | 1.55 | 2.29 | 0.62 | 0.41 | 0.69 |
  | ConfDiff | 0.54±0.00 | 0.85±0.00 | 2.70±0.01 | 1.44±0.00 | 2.22±0.04 | 0.64±0.00 | 0.40±0.00 | 0.67±0.00 | | ConfRover | 0.51±0.01 | 0.85±0.00 | 2.66±0.02 | 1.47±0.03 | 2.23±0.04 | 0.62±0.01 | 0.37±0.01 | 0.66±0.01 | | MDGen | 0.47±0.04 | 0.72±0.02 | 2.78±0.04 | 1.86±0.03 | 2.44±0.04 | 0.51±0.01 | 0.28±0.01 | 0.57±0.01 |

With the updated results, we confirm the following: (1) In forward simulation, ConfRover outperforms MDGen in predicting dynamic levels, capturing major motions, and recovering conformational states. (2) For time-independent conformation generation, ConfRover performs on par with specialized models such as AlphaFlow and ConfDiff. Its performance on metrics including 'per-target RMSF r', 'RMWD', 'MD PCA W2', 'Joint PCA W2', 'Weak contacts J', and 'Exposed residues J' is generally within one standard deviation or better, compared to ConfDiff and AlphaFlow.

Weakness 2: Inference time metrics comparisons with MD simulation.

While we briefly discussed inference time in Appendix A.2, we recognize the importance of providing more detailed comparisons with typical MD simulation runs. Below, we include a detailed runtime analysis comparing ConfRover and MD simulations, using the same hardware (NVIDIA H100-80G). Specifically, we measured the wall-clock time required to generate 100 ns ATLAS trajectories (80 frames) for proteins of varying sizes and report the average inference time per size bucket. For comparison, we also selected a representative protein from each bucket and estimated the time required to simulate 100 ns using OpenMM with implicit solvent.

As shown in the table, ConfRover provides clear speedup for 100ns simulation, with even more pronounced acceleration for larger proteins. Beyond faster simulation with larger strides, ConfRover also supports time-independent sampling for generating independent conformations in parallel, and interpolation between terminal conformations, capabilities that are not easily achievable with classical unbiased MD simulations. While targeted MD simulations could in principle be used for transition pathway sampling, implementing and benchmarking such setups is beyond the scope of this short rebuttal period. Nonetheless, we believe the reported unbiased MD simulation speeds offer a concrete and fair basis for comparing inference efficiency, and they highlight the practical advantages of ConfRover.

Weakness 3: unification of tasks

Thank you for bringing this up. By "unification" we refer to a shared modeling framework that can learn from multiple tasks, rather than a single model that performs all tasks equally well out of the box. While training a single model for all three tasks is possible, different training strategies often yield models with varying strengths. In our early experiments, we trained a single model jointly on three tasks, but observed slightly degraded performance on time-independent sampling (e.g., on contact prediction). As a result, we adopted a two-stage training strategy, continuing training for interpolation to better balance task performance.

Other comments

1. Methods part being too dense. We are sorry that the reviewer found the Methods section difficult to follow. Due to page limitations, we had to condense some technical content and move certain model details (e.g., SE(3) diffusion) to the supplementary materials. With additional space available in the final version, we aimed to provide smooth reading experience for readers from diverse backgrounds. We would greatly appreciate any specific suggestions to help us strengthen the revised manuscript.

2. Limitations on modeling complexes and interactions. We appreciate the reviewer for pointing out this important limitation. While the ConfRover framework is architecture agnostic and can, in principle, incorporate more advanced components such as AlphaFold3-style encoder-decoders for modeling complex interactions, the current implementation does not explicitly model such interactions. Additionally, a key challenge in this direction is the scarcity of high-quality datasets capturing interaction dynamics. We have identified promising datasets such as MISATO [1], which include protein-ligand interaction trajectories. We will acknowledge this limitation in the revised manuscript and highlight it as an important avenue for future work.

3. Comparison with MLFF. Thanks for the suggestion. ConfRover differs from machine learning force fields (MLFFs) in terms of the trade-off between accuracy and efficiency, as well as the timescales targeted. MLFFs, such as MACE-OFF and Orb, are designed to integrate high-level quantum accuracy into classical molecular dynamics (MD) simulations, aiming to improve accuracy while retaining scalability. However, these models still rely on MD-like sequential sampling with small integration steps (fs level) and are often more computationally expensive than classical MD, hindering their ability to efficiently capture long-timescale conformational changes. In contrast, dynamic generative models like ConfRover are tailored for capturing slower dynamics on longer timescales, such as ps to ns. In addition, ConfRover enables non-sequential sampling strategies, including time-independent conformation generation and interpolation between terminal states, making it well-suited for exploring broad conformational landscapes. We will add this to discussion.

[1] Siebenmorgen T, Menezes F, Benassou S, et al. MISATO: machine learning dataset of protein–ligand complexes for structure-based drug discovery. Nat Comput Sci. 2024;4(5):367-378.

We thank the reviewer for affirming our manuscript as well-written, well-organized, and pleasant to read, and for recognizing the value of our insights and discussions, as well as the soundness of our results.

Below are our responses to the questions and weaknesses raised:

Q1: Relations and differences with two-for-one

We appreciate the reviewer for bringing the "Two-for-One" paper to our attention. While both Two-for-One and ConfRover explore the relationship between conformational distributions and dynamics using diffusion-based generative models, their focuses and methodologies differ: Two-for-One does not explicitly learn a temporal generative process $p(x|x^{<l})$; instead, it uses a score function learned via diffusion as an approximate coarse-grained force field and requires simulating dynamics through MD; In contrast, our model directly captures both the static distribution $p(x)$ and temporal dynamics $p(x|x^{<l})$ within the generative framework itself, allowing us to generate both time-correlated and uncorrelated samples via diffusion.

Nonetheless, we find the Two-for-One paper insightful in unifying distribution learning and dynamics generation from a physics perspective, and we will include it appropriately in the revised manuscript.

Q2: ConfRover does not explicitly consider velocity

It is correct that velocity is not explicitly encoded in ConfRover, as it is absent in ATLAS. As a result, the model relies solely on temporal relationships between coordinate frames. However, we expect the attention-based temporal module to infer higher-order motion information, akin to velocity, by reasoning over coordinate differences and time intervals between frames. Unlike velocity, which captures local changes over short time scales, frame-to-frame differences across multiple scales may provide richer dynamic information. Yet, explicit velocity data could offer additional guidance on motion direction, and we would be happy to explore its potential benefits when such data becomes available in future datasets.

Q3: FrameEncoder does not contain temporal information

In ConfRover, the FrameEncoder encodes only structural information, while temporal information is incorporated separately in the temporal module using rotary position encoding (RoPE) [1]. Specifically, we encode time as discrete snapshot indices (e.g., 128, 256, 384, ...) corresponding to each frame (0, 1, 2, ...). We use RoPE for temporal encoding based on two key considerations: (1) It enables the model to learn dynamics at real temporal scales, matching the snapshot interval resolution (e.g., 10 ps in ATLAS). (2) Unlike hard-coding time into frame-level embeddings, RoPE encodes relative time rather than absolute time, maintaining invariance under global time shifts.

While we intentionally avoid injecting absolute time into the FrameEncoder, it may be beneficial to encode the trajectory "stride" to enhance multi-scale learning. We leave this direction for future investigation.

Weakness 1: The method is relatively simple

We consider the simplicity of our model a merit rather than a weakness. Despite its simple form, the core idea of learning different perspectives of the protein conformational landscape via conditional probability is carefully designed so that we can use a modern causal language model architecture enables a unified and flexible approach across multiple protein conformation tasks.

Weakness 2: the evaluation are not standard

This is an inherent challenge in developing models for protein dynamics, and we see it as a potential contribution of our work. Standardized evaluation protocols are lacking for this problem, especially for large proteins where the MD trajectory are not fully equilibrated. We designed metrics to capture aspects of dynamic behavior as comprehensively as we can. Our evaluation assesses how models respond to different initial conformations and time scales and, for long-time simulation, whether they capture main dynamics and recover conformational states.

During the rebuttal, we also added structural quality and energy-based evaluations using standard pipelines to complement our analysis, particularly on whether generated conformations are plausible. Specifically, we used MolProbity [2] to assess geometric accuracy and MadraX [3] for heavy-atom energy evaluation. We evaluated 38 cases tested in forward simulation and conformation interpolation tasks, and compare across different models. Results are summarized below (all values reported as mean ± std; energy values as 95% percentile ranges). It shows both ConfRover (forward simulation) and ConfRover-interp have similar structural quality, comparable to MD references in backbone dihedral (Ramachandran), bond geometry, and overall energy. While there are more clashes detected than MD references, it also depends on ad hoc hydrogen addition and may bias evaluation of heavy-atom-only models. Overall, ConfRover consistently outperforms MDGen across all metrics.

We hope these efforts provide a comprehensive understanding of ConfRover and inform future benchmarks.

Minor points:

• Clarification of Figure 1A (iii): This figure illustrates how we condition on both the first and last frames in the causal sequence model. The second box represents frame 0, the original first frame, and the first box represents the last frame (arrows indicate moving it to the front of the sequence). Both boxes have black outlines to mark them as conditioning frames. We will clarify this further in the revised manuscript.
• We thank the reviewer for pointing out typos and will correct them in the revision.

[1] Su, Jianlin, et al. "Roformer: Enhanced transformer with rotary position embedding." Neurocomputing 568 (2024): 127063. [2] Williams CJ, Headd JJ, Moriarty NW, et al. MolProbity: More and better reference data for improved all-atom structure validation. Protein Sci. 2018;27(1):293-315. [3] Orlando G, Serrano L, Schymkowitz J, Rousseau F. Integrating physics in deep learning algorithms: a force field as a PyTorch module. Bioinformatics. 2024;40(4):btae160.

We appreciate the reviewer's recognition that our work addresses important tasks and the proposed autoregressive framework for multiple tasks sensible. We also thank the reviewer for their valuable input and constructive feedback. We organize our response as follows:

Weakness 1: originality and relation to similar ideas

The key contribution of this work is the introduction of a typical autoregressive framework $p(x|x^{<l})$ into the modeling of MD trajectories. We demonstrate that this formulation naturally aligns with several important tasks in protein conformation sampling by managing sequential dependencies across frames. By leveraging modern causal transformers, ConfRover offers efficient training and can be readily extended to generate longer trajectories.

• vs MarDini: While ConfRover shares the general idea of combining autoregressive modeling with diffusion, there are key differences. First, the two methods target fundamentally different application domains. MarDini focuses on video data, whereas ConfRover is designed for molecular dynamics simulations. Second, ConfRover emphasizes a broader multi-task setting, including time-independent sampling and interpolation tasks, which were not explored in MarDini.
• vs AlphaFolding: While AlphaFolding extends MD trajectories by iteratively generating fixed-size blocks conditioned on motion and reference frames, our causal autoregressive model differs in key ways: (1) ConfRover generates long trajectories frame-by-frame using KV-cache, unlike AlphaFolding’s block-wise extension that discards historical context. (2) ConfRover operates at the frame level with clear causal dependencies, whereas AlphaFolding’s block-level autoregression lacks explicitly defined intra-block causality. (3) ConfRover supports forward simulation, time-independent sampling, and interpolation - capabilities not directly supported by AlphaFolding.
• Reuse existing components: This work focuses on proposing a general autoregressive framework. To demonstrate this idea, we intentionally use well-established architectural components. Architectural improvements are beyond the scope of this paper but represent a promising direction for future work.

Weakness 2: conformation evaluation and baseline comparison

1. Physically grounded evaluation. thank you for the suggestion. We agree that demonstrating the physical plausibility of generated conformations is important. To this end, we introduced standard structural and energy evaluation pipelines using MolProbity [1] for geometric quality and MadraX [2] for heavy-atom-based energy assessment. We compared conformations from reference MD, MDGen, and ConfRover (in both forward simulation and interpolation settings). All structures were evaluated using the default settings of MolProbity and MadraX. We found that energy and structural metrics can be sensitive to minor deviations and it is necessary to apply local relaxations even for MD reference conformations. We applied the standard protocol from OpenFold to all conformations to ensure fair comparison and reliable energy estimates. Results are summarized in the following table (values are reported as mean ± std; energy values as 95% percentile ranges):

The results show that ConfRover generates high-quality conformations, matching MD references in backbone dihedrals, bond geometry, and energy, while outperforming MDGen across all metrics. Interpolation quality: when comparing ConfRover-interp with ConfRover-fwd, they shows similar structural quality, indicating the conformation generated from interpolation maintain physically plausible.

2. Dihedral flexibility analysis. While prior results suggest the conformations are physically plausible, we additionally performed dihedral flexibility analysis as suggested by the reviewer. We extracted dihedral angles from the 100 ns simulations and computed their circular variance. Pearson correlation with the MD reference was used to assess how well the model captures ground-truth flexibility. The result shown below shows reasonable agreement between ConfRover generated sample and MD reference.

3. Comparison with other models like AlphaFolding. The lack of baseline models is a common challenge in this field. We contacted the authors of AlphaFolding to request their model for comparison, but the weights are not available at this time. However, we identified code from a related open source project and are currently working on retraining their model for evaluation on the ATLAS benchmark. We are happy to update our results if preliminary comparisons become available during the discussion phase.

Weakness 3: potential data leakage from OpenFold model

Our objective is to model the distribution and dynamics of protein conformations, not to predict a single folded structure. Accordingly, our setup and evaluation metrics focus on structural variation and temporal behavior rather than alignment to a fixed reference. Since OpenFold is trained on static PDB structures and lacks such dynamic information, we do not believe data leakage is a concern under the current setting.

Questions:

1. Data diversity conditioned on the same conditioning frames. We are currently investigating the diversity of frame-conditioned generation and will share updated results during the discussion phase.

2. Regarding energy conservation or implied timescales against MD. Implied timescales are commonly used in Markov State Models (MSMs) to characterize the dynamics of equilibrated systems. However, the MD trajectories in ATLAS are not well equilibrated, making standard implied timescale analysis unreliable in this context. To address this limitation, we instead analyze the dominant tICA component across varying lag times (Figure 5A) as a proxy. We are currently investigating energy conservation during trajectory generation using the newly integrated MadraX and will update the relevant results during the discussion phase.

3. CA clash peptide bonds quality metrics. We calculated the CA clash/break rate and peptide bond break rate following the evaluation code of ConfDiff [3]. Specifically, CA clash is determined when the distance of two alpha carbon atoms are within 2 * 1.7 - 0.4 = 3.0 Å, and CA break is determined if CA of two consecutive residues are greater than 3.8 + 0.4 = 4.2 Å. For peptide bond, we consider a broken peptide bond with have bond length greater than 1.4 Å. As discussed in the response to Weakness 2, we have include a standard set of protein conformation quality evaluation using MolProbity.

4. Conformation sampling for proteins with stable alternative locations. We thank the reviewer for bringing this work to our attention. The referenced paper presents challenging protein cases where conformational changes are difficult to sample using state-of-the-art generative models. As the benchmark includes experimental data that differs from the MD-based benchmark we use, we are currently investigating these cases and are willing to share results if obtained during the discussion period.

[1] Williams CJ, Headd JJ, Moriarty NW, et al. MolProbity: More and better reference data for improved all-atom structure validation. Protein Sci. 2018;27(1):293-315. [2] Orlando G, Serrano L, Schymkowitz J, Rousseau F. Integrating physics in deep learning algorithms: a force field as a PyTorch module. Bioinformatics. 2024;40(4):btae160. [3] https://github.com/bytedance/ConfDiff

I thank the authors for the very detailed responses. Most of the concerns are somewhat addressed (although the empirical evidence does suggest ConfRover is not tremendously better than other existing methods, and dihedral sampling is still far from MD). I will increase my score accordingly.

We thank the reviewer for acknowledging the significance of our overall design improvements, the strong performance across tasks in transferable settings, and the significant value of introducing the causal transformer for researchers in the field. Here we include our point-to-point response to the questions raised:

Q1: Encoding of MD timesteps.

The MD timestep is encoded in the Llama layer of the TemporalModule using rotary position encoding (RoPE) [1]. Specifically, we represent time as discrete snapshot indices (e.g., 128, 256, 384, ...) corresponding to frame indices (0, 1, 2, ...). RoPE allows the model to learn dynamics across multiple temporal scales and, by encoding relative rather than absolute time, ensures invariance to global time shifts. In our multi-start experiments, we observe that the diversity of generated trajectories increases with larger stride values (see below), highlighting the model's ability to capture scale-dependent dynamics:

Q2: Frame settings for training and evaluation.

We train models on sub-trajectories of 8 frames sampled from original MD. For evaluation of different tasks: 9 frames for multi-start and conformation interpolation, 80 frames for Atlas-100ns simulation, and one frame for time-independent sampling

Q3: Model equivariance.

We did not require data augmentation thanks to the use of invariant sequence and structure embeddings, SE(3)-diffusion, and equivariant denoising models. Specifically, the encoding layer is invariant to global translations and rotations: it encodes input structures via pairwise distances between pseudo-beta atoms, and the resulting single and pair embeddings are invariant, enabling invariant reasoning in the TemporalModule. For the decoder, we adopt Invariant Point Attention from AlphaFold, which predicts residue rigid-body updates relative to the input structure, making the denoising network equivariant to global rotations.

Q4: Additional quality metrics.

Thank you for the suggestion. We have added detailed structural quality and energy evaluation of generated intermediate states. Specifically, we used MolProbity [2] to assess geometric accuracy and MadraX [3] for heavy-atom-only energy evaluation. To verify whether interpolation tasks still generate physically plausible conformations, we evaluated the intermediate conformations (excluding the first and last frames), labeled ConfRover-interp, and compared them to conformations from forward simulations (without terminal constraints, labeled ConfRover-fwd) and reference MD simulations (oracle). All structures were processed using constrained local relaxation and evaluated with the default settings of MolProbity and MadraX. We found such relaxation necessary to obtain accurate energy evaluations, even for MD references. Results are summarized in the following table (all values reported as mean ± std; energy values as 95% percentile ranges):

• Comparing ConfRover-interp to ConfRover-fwd, we observe similar structural quality, suggesting that interpolated conformations are physically realistic. Slightly higher energy in interpolated samples may reflect the presence of regions with energy barriers.
• Other comparisons show ConfRover generates conformation with high quality. ConfRover achieves comparable performance to MD references in backbone dihedral (Ramachandran), bond geometry, and overall energy. The largest discrepancy lies in clash scores, which depend on ad hoc hydrogen addition and may bias evaluation of heavy-atom-only models. ConfRover consistently outperforms MDGen across all metrics. | exp | Ramachandran outliers % | Ramachandran favored % | Rotamer outliers | Clashscore | RMS(bonds) | RMS(angles) | MolProbity score | MadraX Energy | |-------------------|--------------------------|--------------------------|-------------------|-------------|-------------|---------------|-------------------|----------------------------------------| | MD Reference | 0.38±0.49 | 97.41±1.49 | 1.02±0.89 | 0.04±0.16 | 0.01±0.00 | 1.88±0.05 | 0.72±0.18 | -519.3 (-1793.0, -53.4) | | MDGen | 0.93±0.86 | 94.98±2.04 | 2.86±1.59 | 16.14±20.05 | 0.02±0.02 | 2.13±0.30 | 2.24±0.40 | -314.7 (-1483.8, 263.6) | | ConfRover-fwd | 0.58±0.63 | 96.93±1.45 | 1.98±1.48 | 7.81±6.52 | 0.01±0.01 | 1.88±0.25 | 1.72±0.38 | -522.2 (-1858.9, -53.4) | | ConfRover-interp | 0.71±0.94 | 96.90±1.95 | 1.86±1.46 | 7.25±8.74 | 0.02±0.01 | 1.91±0.32 | 1.61±0.51 | -469.7 (-1712.3, -42.8) |

Q5: inference time across different protein sizes.

We measured the wall-clock time (minutes) required to generate 100 ns ATLAS trajectories (80 frames) for proteins of varying sizes and report the average inference time per size bucket. For comparison, we also selected a representative protein from each bucket and estimated the time required to simulate 100 ns using OpenMM with implicit solvent. As shown on the table below, ConfRover can sample at least 10x speedup over implicit solvent MD simulations. The acceleration becomes more pronounced as protein sizes increases, suggesting ConfRover might be more advantageous for larger proteins. Notably, the cost of generating additional frames remains nearly constant due to our autoregressive generation with KV-caching, which eliminates redundant computation of attention activations.

Weakness 1: Heavy architecture.

The detailed computational cost of applying ConfRover to larger proteins is summarized in our response to Q5. We agree that standard architectures in the field, such as Pairformer, are computationally intensive. However, designing efficient neural architectures for protein structure modeling remains a broad challenge in the field. In this work, our focus is on proposing a framework for learning protein dynamics, rather than advancing neural architectural innovations. Therefore, we adopt proven architectures to build ConfRover, which demonstrates competitive performance, scalability to proteins with over 700 amino acids, and reasonable acceleration compared to MD. As the reviewer noted, recent acceleration libraries such as cuEquivariance [4] could be beneficial for further speeding up our model, and we will consider integrating them in future work.

Weakness 2: Lack statistical analysis of dynamics.

Unlike Timewarp or EquiJump, which focus on small systems with well-equilibrated dynamics, our work specifically targets modeling dynamics for large proteins in transferable settings. As noted in MDGen, trajectories in ATLAS are not fully equilibrated, making it difficult to take the Markov state models (MSMs) approach for evaluating long-term dynamics.

Due to this limitation, we additionally designed experiments and metrics to assess whether the model captures dynamic changes across different time scales and initial conditions (multi-start benchmark) and whether major dynamic modes are correctly reflected (as in the TICA analysis in Figure 5). While these metrics are not perfect, we believe they provide statistical insights into the dynamic behavior of the models and are effective in revealing some limitations of current state-of-the-art approaches.

Weakness 3: Significance of a unified framework.

A unified framework for protein conformational dynamics is appealing for several reasons. First, tasks like forward simulation, interpolation, and time-independent sampling share similarities, naturally to address in a single framework. Second, both time-dependent and independent conformations stem from the same underlying distribution, as also noted in prior work [5], supporting joint learning. Third, our framework’s ability to leverage both structures and trajectories enables flexible training and paves the way for foundation models in protein conformations.

While alternative approaches like stochastic interpolation are possible, our early experiments with them were unsuccessful. In contrast, our autoregressive LLM + diffusion model performs robustly across tasks and offers a strong basis for learning conformational dynamics.

Finally, we clarify that ConfRover adds minimal overhead for structure generation: the temporal module is lightweight, and for time-independent tasks, it reduces to a simple MLP. This design enables dynamic modeling with little additional cost over the conformation diffusion model.

[1] Su, Jianlin, et al. "Roformer: Enhanced transformer with rotary position embedding." Neurocomputing 568 (2024): 127063.

[2] Williams CJ, Headd JJ, Moriarty NW, et al. MolProbity: More and better reference data for improved all-atom structure validation. Protein Sci. 2018;27(1):293-315.

[3] Orlando G, Serrano L, Schymkowitz J, Rousseau F. Integrating physics in deep learning algorithms: a force field as a PyTorch module. Bioinformatics. 2024;40(4):btae160.

[4] cuEquivariance: https://docs.nvidia.com/cuda/cuequivariance/

[5] Arts M, Satorras VG, Huang CW, et al. Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics. http://arxiv.org/abs/2302.00600