Align Your Structures: Generating Trajectories with Structure Pretraining for Molecular Dynamics
Authors: Aniketh Iyengar
Jiaqi Han
Pengwei Sun
Mingjian Jiang
Jianwen Xie
Stefano Ermon
Venue: ICLR 2026 Poster (2026)
Keywords: geometric diffusion models
molecular dynamics
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Generating molecular dynamics (MD) trajectories using deep generative models has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-dimensional MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pre-training for MD trajectory generation. Specifically, we first train a diffusion-based structure generation model on a large-scale conformer dataset, on top of which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simulation, and interpolation tasks, and further extend our framework and analysis to tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.

Published as a conference paper at ICLR 2026
ALIGN YOUR STRUCTURES: GENERATING TRAJECTO- RIES WITH STRUCTURE PRETRAINING FOR MOLECU- LAR DYNAMICS
Aniketh Iyengar** Jiaqi Han Pengwei Sun Mingjian Jiang' Jianwen Xie Stefano Ermon Stanford University LLabbda, Inc
ABSTRACT
Generating molecular dynamics (MD) trajectories using deep generative mod- els has attracted increasing attention, yet remains inherently challenging due to the limited availability of MD data and the complexities involved in modeling high-ding nigh-dimenssonal MD distributions. To overcome these challenges, we propose a novel framework that leverages structure pretraining for MD) trajectory genera- tion. Specifically, we first train diffusion- based structure generation model on a large-scale conformer dataset, on top which we introduce an interpolator module trained on MD trajectory data, designed to enforce temporal consistency among generated structures. Our approach effectively harnesses abundant structural data to mitigate the scarcity of MD trajectory data and effectively decomposes the intricate MD modeling task into two manageable subproblems: structural generation and temporal alignment. We comprehensively evaluate our method on the QM9 and DRUGS small-molecule datasets across unconditional generation, forward simu- lation, and interpolation tasks, and further extend our framework and analysis tetrapeptide and protein monomer systems. Experimental results confirm that our approach excels in generating chemically realistic MD trajectories, as evidenced by remarkable improvements of accuracy in geometric, dynamical, and energetic measurements.
INTRODUCTION
Molecular Dynamics (MD) is computational method used to model the physical motions of atoms and molecules over time (Alder & Wainwright, 1959; Verlet, 1967). Numerically integrating Newton's equations of motion, MD simulates the temporal evolution of molecular systems at atomic resolution. It has become a widely adopted tool in biology (McCammon et al., 1977), chemistry (Rahman, 1964), and materials science (Antalík al., 2024). However, MD can be computationally demanding. often requiring long simulation times and many small integration steps, especially for physio- realistic dynamics. This cost has motivated extensive work on accelerating MD and improving sampling efficiency (Shaw et al., 2009; Darden et al., 1993; Laio & Parrinello, 2002). Moreover, advances in biomolecular engineering increasingly leverage machine learning to design molecular systems (Jumper et al., 2021; Passaro et al., 2025; Powers et al., 2025), highlighting its importance in drug discovery. In this context, deep generative models especially diffusion models (Noé et al., 2019; Jing et al., 2024a; Klein al., 2023)-1 have emerged as effective surrogates for capturing the complex and diverse distributions observed in MD simulations.
Despite their promise, identify factor that poses remarkable limitations on their utility. The MD generative models are typically optimized on single or limited number of molecular systems (Noé al., 2019; Han al., 2024; Jing al., 2024c), making it fundamental challenge for them to generalize across arbitrary molecules. Two main factors contribute to this issue. Data scarcity: Constructing large-scale, physio-realistic MD datasets spanning diverse molecular systems is prohibitively expensive due to the high computational cost of running MD simulations at scale. As result, available training data is insufficient for capturing the full diversity of MD distributions.
Eguul contribution. Correspondence to jiagi han@stanford.eee Code is available at https: //gi thub. com/ani 11452/A1 (e/22/Algg_/i. _tt__ooorrttsttreeeeeeee

---

Published as a conference paper at ICLR 2026
Structure Pretraining
EGInterpolator
Structure
Temponl
Strueture
Remposs
Ee
N(O.I)
P5
N 1,
T
e N(O.))
gmm (x!Ti) MD Fine-tuning
Figure 1:
The overall two-stage framework of EGINTERPOLATOR, Structure pretraining: We first pretrain a conformer model Ep on a large-scale conformer dataset. MD fine-tuning: The model then combined with additional temporal interpolator h to approach the MD distribution pnd (x(T)).
Modeling complexity: MD data extends the molecular structure space with an additional temporal dimension, making it inherently high-dimensional. This significantly increases modeling difficulty, especially when models must preserve both structural fidelity and realistic dynamical behavior.
In this work, we propose novel approach named EGINTERPOLATOR that addresses the challenges through structure pretraining. Specifically, we decompose the MD modeling problem into two sequential subtasks. First, train conformer diffusion model to generate conformers-i.e. plausible molecular structures corresponding to frames along an MD trajectory-usinng large-scale conformer datasets. Building on this pretrained structure model, we then initialize additional temporal layers and integrate structural and temporal information through novel module called the equivariant temporal interpolator. We theoretically show that the temporal interpolator implicitly models a transition from temporally independent structural distribution to the fully correlated MD distribution. This formulation alleviates optimization difficulty by decoupling spatial and temporal learning, which enables (1) more efficient learning of dynamics from limited MD data through the temporal interpolator, and (2) generation higher-fidelity, physically realistic molecular poses implicitly constrained by the pretrained structure module.
Our approach directly addresses three central challenges. First, mitigates MD data scarcity by leveraging large-scale conformer datasets with diverse molecular structures, complementing small- scale MD data and improving generalization to unseen molecules. Second, it ensures structural and energetic fidelity by grounding trajectory generation in a pretrained conformer model, which provides a foundation for downstream dynamics. Third, the two-stage pipeline decomposes the complexity of modeling nigh-dimensional MD distributions into two manageable tasks: learning the distribution of independent frames and subsequently capturing their temporal dependencies.
Contributions. We identify key challenges in the generalization of MD diffusion models and propose structure pretraining as a remedy. 2. We develop a principled training framework based on structure pretraining and validate it on small molecular systems. 3. We introduce the equivariant temporal interpolator, module for learning temporal dependencies across frames. 4. We evaluate our framework on unconditional generation, forward simulation, and interpolation, showing accurate modeling of MD distributions while preserving conformer generation quality across small molecules, tetrapeptide, and protein monomer systems.
2 RELATED WORK
Geometric diffusion models. Generative models for geometric data have garnered increasing attention across multiple domains. In molecular generation, GeoDiff (Xu et al., 2022) pioneered for conformer generation while EDM (Hoogeboom et al., 2022b) operates on both continuous coordinates and categorical atom types. Subsequent works (Xu et al., 2023; 2024a) introduced structured latent spaces to enhance scalability and controllability. For larger molecules, GCDM (Morehead & Cheng, 2024) incorporated ecometry-complest local frames and chirality features into SE(3)-equivarian networks. EBD (Park & Shen, 2024) performs hierarchically by first sampling scaffolds before refining atom positions through blurring-bar based denoising. Yet, they only model static structures while in this work we study the problem of their temporal correlation in MD.
2

---

Published as a conference paper at ICLR 2026
Molecular Structure Datasets & Sampling. Large-scale structural datasets central to molecular modeling. Some, like the Protein Data Bank (PDB) (Berman et al., 2000), archive experimentally resolved biomolecular structures, while others, such as GEOM (QM9 and Drugs) (Axelrod & Gomez- Bombarelli, 2022) and OMol (Levine et al., 2025), provide computationally derived conformer ensembles at scale. The latter can utilize accelerated sampling strategies that emphasize structural diversity while reducing computational cost. For instance, OMol reports many protein-ligand simulations at elevated temperatures, while GEOM employs CREST (Berman al., 2000), coupling the semiempirical GFN2-xTB method (Bannwarth et al., 2019) with metadynamics and geometry optimization. Such approaches broaden structural coverage but trade dynamic accuracy for diversity, highlighting the complementary role of generative models in capturing physio-realistic dynamics.
ML--based Molecular Dynamics. Modeling molecular dynamics challenging due to complex multi- body interactions, data scarcity, and high-dimensional state spaces. Equivariant architectures such as EGNN (Satorras al., 2021b) and Trans-ore (Fuchs et al., 2020) improve generalization by embedding physical symmetries (Brandstetter et al., 2022; Xu et al., 2024b), while autoregressive approaches like Timewarp (Klein et al., 2023) and EquiJump (dos Santos Costa et al., 2024) capture temporal transitions but suffer from error compounding and limited design flexibility. Diffusion- based methods address these issues by modeling trajectories holistically: GeoTDM (Han et al., 2024) enforces equivariance but requires molecule-specine training, and MDGen (Jing et al., 2024b) extends to peptide torsions with flow-based modeling but relies on key-frame conditioning. In contrast, our method generalizes more readily across arbitrary molecular systems.
Video Generation from Image Models. Blattmann et al. (2023) highlighted extending image diffusion models videos by adding temporal layers, an idea motivating our spatial-temporal decoupling. Related work in latent image diffusion (Rombach et al., 2021) and holistic video generation (Brooks et al., 2024) further demonstrate the scalability of spatiotemporal diffusion.
PRELIMINARIES
Geometric representation of molecular dynamics. In this work, we represent each molecular dynamics trajectory as a collection of static structures, or equivalently conformers that evolve through time. Each frame of conformer at timestep f is viewed as geometric graph g(t) == (h, x(,xx)) E) where each row h; E R " is the node feature of atom such as its atomic number, x! E R is the Euclidean coordinate of atom i at timestep I,, and is the set of edges induced by the chemical bonds between atoms. The trajectory with length T' is correspondingly represented x! : x (0:T- E T
Geometric diffusion model for conformer generation. Geometric diffusion models (Xu et al., 2022; Hoogeboom et al., 2022a; Xu et al., 2023) are family of diffusion- generative mod- els (Sohl-Dickstein et al., 2015; Ho et al., 2020a; Song & Ermon, 2019; Song et al., 2021) ded- icated to capture the distribution of static conformer structures p(x[h, E), given the configura- tion of the molecular graph specified by the node feature h and edge connectivity E. Inherit- ing the framework of diffusion models, they feature Markovian forward noising process that gradually perturbs Xo toward XT through T diffusion steps, with the Gaussian transition ker- nel (x,, xy-1) = Nxx; /1 -,,,-11, B,1), where 3, is the noise schedule such that x is close to the Gaussian prior (O, I). The reverse process denoises toward the clean data using po(x+-1 (x,) N ((x-11i (x(; T), I.).. The model is optimized via Ho et al. (2020a):
Lcout
IE <x(xx,-)]
(1)
where Doonf is the conformer dataset, X, = Vā + VI ā,e with ã, being certain noise schedule and co parameterizes the mean by oo (x+: (x,: Va,
1 (x, v/= _ cx(xx, A eritical property of geometric diffusion models lies in the -33aa-nie of their marginal i.e., Pe (xp)) = g (xo), E SE(3), where is an arbitrary group action in SE(3) that consists of all 3D rotations and translations, and pe (xx) = p(x7) II_ Pe (x,-1 xx, ). This is achieved by parameterizing Eg with an equivariant graph neural network (Satorras et al., 2021 such that g Ex(x,, r) = Ee(g x,, which guarantees the -qqiivarnne of the transition kernel px(x--1|x; (x)) at each step т.
For conciseness henceforth omit the conditions h. E in p(x unless otherwise specified.
3

---

Published as a conference paper at ICLR 2026
Problem definition. In this work, seek to design diffusion model that captures the distribution of molecular dynamics ymd given node features h and edges &. Based on this goal, we are additionally interested in two relevant subtasks, namely forward simulation, which models the conditional distribution (x((1 (x(0)) given the initial structure x("), and interpolation, which models pnn (x(1:T-2) (x(x)) x xTT-1)) given both the initial frame x()) and final frame x(T-1).
4 METHOD
In this section, present approach for generating MD trajectories by temporally aligning structural distributions. 4.1 introduces the overall framework conformer pretraining and temporal alignment; $ 4.2 describes the temporal interpolator that couples conformer and temporal layers; and $ 4.3 details the implementation of EGINTERPOLATOR.
4.1 TRAJECTORY GENERATION BY ALIGNING STRUCTURE MODEL
Motivation. While substantial research has advanced the modeling of empirical conformer data distribution p (x), generalizing this paradigm to molecular dynamics trajectories remains inherently challenging for two primary reasons. 1. Data scarcity. Unlike conformer modeling, which benefits from extensive datasets (Ramakrishnan et al., 2014; Axelrod &
2022), molecular dynamics simulations incur prohibitive computational costs. Consequently, existing MD datasets (Chmiela et al., 2017; Meersche et al., 2024) are typically constrained to limited molecular classes, significantly restricting generalizeability across more arbitrarily defined molecular types. 2. Modeling complexity. MD trajectories inhabit high-dimensions spaces with an additional temporal dimension.
The inherent complexity of the joint distribution p=d( (xl" is further exacerbated by data scarcity, insufficient training samples create greater sparsity in the digennimensional data support, thereby complicating accurate density estimation.
Our solution. We propose to leverage pretrained conformer diffusion model and transform it into an MD generation model, by stacking additional trainable temporal layers to enforce temporal consistency along each MD trajectory. Formally, given a pretrained conformer diffusion model ég inducing the marginal pž (x). we devise eg,0 for modeling the MD distribution padd (xl?1), where represents parameters in the additional temporal layers, indicating that the MD generative model with parameter set {0, ) is partially initialized from the pretrained structure model 0. The MD diffusion model is then optimized on the MD trajectory dataset with the diffusion loss
Lad = E (1)) (
-Ep
and (x!"") .)
(2)
where x!7
x a and cT E RTxNx3 is the Gaussian noise and D is
MD dataset. Our proposal effectively addresses the core challenges. We mitigate MD data scarcity by initializing with conformer model trained on large-scale conformer datasets, transferring generalization capability to unseen molecules. Furthermore, our two-stage pipeline decomposes the complex modeling of udd (x!Tl) into manageable subproblems: conformer pretraining first models each frame independently, yielding an intermediate trajectory-level distribution (x(T)) =
IT p (x(1)) that does not incorporate any temporal correlation. The second stage introduces additional parameters è to capture the temporal dependency across different frames, leading to the joint distribution pord (x (1)). This approach efficiently offloads the complexity by using gnd (xl21) as an anchor. The flowchart of our proposed framework is depicted in Fig. 1.
4.2 TEMPORAL INTERPOLATOR
With the proposed framework, it still yet unrevealed how to allocate the additional parameters á to capture the temporal dependency across frames for aligning the structures into an MD trajectory. To this end, we introduce a novel temporal interpolator module that entangles the pretrained structure denoiser egt with the additional temporal network e through a linear interpolation:
.nd (x(") 7) = and + (1 - a)e² (x!?) 2nd -), 000
s.t. amd = (x("
(3)
4

---

Published as a conference paper at ICLR 2026
where or E IR is the interpolation coefficient, and [eo(x.) - is the concatenation along the temporal axis for the outputs eü (x+ (t) at frames 0 S t t T' 1, and 2 E (x7 eund .) = 5% (x (T)
(2)
amd r) - x, [Ti where s is an equivariant temporal attention network (Han et al., 2024).
tP
Intuitively, Eq. 3 mixes the output from the structure model eşp together with the the temporal model 6% as the final output end making it both structural and temporal semporal-aware. Notably, compared with other mixing strategies, our design has several unique benefits, as we analyzed below.
We start by showing that the interpolation mechanism in Eq. 3 implicitly induces an intermediate distribution for the temporal network to learn. We reveal such insight the following theorem.
Theorem 4.1. Suppose eø perfectly models pe (x) and Eg perfectly models (xl"xx) then the interpolation in Eg. 3 implicitly induces the distribution (x( pmdd 1 (x(rT)) 11- for CΦ. where 8 = 1-a and fmd -I[ pf (x(1).
Temporal interpolator reduces training overhead. Instead of directly matching the highly complex MD distribution ymd (x!2"), the temporal network is now expected to model an intermediate transition between the frame-independent distribution (mnd(((T)) obtained from the structure model and the target MD distribution p pndd (x("T), with I-a defining the weight. By this means, we relieve from
the optimization difficulty for learning the MD distribution by leveraging the interpolation (xl as the stepping stone, while also effectively taking advantage from the conformer pretraining by incorporating pa (x(1)) using pmn (x("T) as the bridge. The effectiveness of our design is also supported by the ablation study in Sec. A.8 which shows clear advantage of our approach compared against a naive two-stage separate training.
The parameterization of c."" Another core design lies in that we inherit the output from the structure model, gnnd as the input to the temporal model, instead of only feeding in the original noised trajectory [T] This is beneficial in terms of facilitates the optimization for e.P Consider the extreme case that the frame-independent distribution is close to the MD distribution, gund (x111) x pmd (xlx1), According to Theorem 4.1, we have that the implicit distribution for the temporal model to approach would be gund (x(2")) findd (x. Therefore, equivalently the temporal model only needs to satisfy tp [T .umd, -) 2 gndd, which can be simply realized by S being an identity mapping, according 6o (x7
tp
to Eq. 3. Therefore, negligible optimization effort is required for s
Interpolation coefficient a. To further enhance thr training flexibility, empirically we adopt the parameterization of a = a (lk) where (()) is the Sigmoid function to ensure smooth interpolation, where & is learnable parameter optimized during training.
Temporal interpolator enables flexible inference. Our design enables two inference modes, Setting suppresses the temporal network, reducing output énd equivalent to independent conformer generation for each frame with batch size T and preserving conformer capability. Using the learned a* restores the full dynamics sampler. Shown in Appendix A.9.2, perturbations of a between these modes also yield meaningful inference behaviors, underscoring the flexibility of our approach.
Temporal interpolator preserves equivariance. Importantly, the linear in- terpolation rule for our temporal interpolator preserves the (proof in Appendix D.2), given the (E33)-qquivariance of both the struc- ture and the temporal models. This property is vital for ensuring the SE(3)- invariance of the marginal, a critical inductive bias to promote data efficiency.
Spatial Layer
Temporal Attention
Spatial Convolution
Cascaded temporal interpolator. Given the justifications for the interpolator, we further explore an extension of our approach by performing such operation in block-wise manner, enabling more expressive information fusion between the pretrained structure model and the additional temporal module. Specificallyy, we perform the interpolation for the output from the structure and temporal model at the [-th block with (t E IR being the coefficient. Furthermore, we also incorporate the interpolation between each layer in the temporal block and the output from the structure block. Detailed flowchart can be found in Fig. 2.
Temporal Attention
Figure 2: Cascaded temporal interpola-
tor block.
5

---

Published as a conference paper at ICLR 2026
A. Coverage and Matching Results QM9 and GEOM-Drun Drugs
B. Generated Conformers
COV-R (%) 1
MAT-R (
COV-P
f
MAT-P (A)
Method
Mcan
Med.
Mean
Med.
Mean
Med.
Mean
Med.
QM0
CONEGF
88.49
94.31
0.2673
0.2685
46.43
43.41
0.5224
0.5124
GRODIFF-A
90.54
94.61
0.2104
0.2021
52.35
50.10
0.4539
0.4399
BASICES
87.62
0,2574
0.2613
58.12
53.24
0,4451
0.4445
Drugs
CONTGF
62.15
70.93
L,1699
1.1596
23.42
15.52
1,7219
1,6663
GEODiPP-A
88.36
96.09
0.8704
0.8628
60.14
61.25
1.1864
1.1391
BASICES
92.35
100.00
0.8340
0.8245
65.59
70.87
1.1389
1,9933
Figure 3: (A) reports performance of BASICES with borrowed numbers from Xu et al. (2022) on SOTA baselines; (B) Example conformers from BASICES on both QM9 & Drugs
Such design inherits the benefits of the interpolator while permitting much denser information flow between the network that evidently improves optimization. We henceforth coin the original design SIMPLE and the cascaded version CASC.
4.3 INSTANTIATION OF EGINTERPOLATOR
Based on the dedicated design of the temporal interpolator in $ 4.2, we describe the overall instantia- tion of our framework following the paradigm depicted in 4.1.
Conformer pretrainings stage. The first stage of our pipeline is the structure pretraining using the large scale conformer dataset Derr For the conformer model cg we resort to Equivariant Graph Convolution Layer (EGCL) (Satorras et al., 2021b) as the basic building block with the update:
x h fES (x, h, E),
(4)
where ES is shorthand for Equivariant Structure layer. The denoiser 6g consists of layers of fES stacked sequentially, and is optimized using the loss Eq. for structure pretraining.
MD training stage. With the pretrained conformer model, we conduct the second stage, the MD training stage with the limited-size MD dataset Dmd, with the additionally initialized temporal network parameterized by stdd. For the temporal network, we utilize the Equivariant Temporal Attention Layer introduced in Han et al. (2024) to capture the temporal dependency with attention:
(5) where ET refers to Equivariant Temporal layer. Each temporal block a stack of three layers- ET at the top and bottom, with an ES layer in the middle-a design that promotes dense entanglement of structural and temporal features. For every ES layer in the pretrained model, we initialize one temporal block; together, these form L interpolator blocks. The model is trained with the trajectory denoising loss (Eq. 2), freezing the pretrained ES layers. This yields a performant MD generative model without degrading conformer generation performance an assurance not achieved in prior work. Appendix A.8.4 details the contribution of the temporal module and MD training, while Appendix A.9, E.8 interpret the learned a values.
x x17], h = fET(x!") (x! h(?l, E),
Forward simulation and interpolation. Our model naturally supports structure-conditioned MD generation: forward simulation conditions on the first frame x0), and interpolation on both x() and (T- Conditioning frames are treated as control signals, passed with noisy frames through the interpolator, and removed before loss computation to ensure the loss is applied only to noisy frames.
5 EXPERIMENTS
We refer to our framework as POLATORP and evaluate its ability to generate realistic MD trajectories for unseen molecules under practical data constraints with limited MD simulations and diverse static structural data. We focus first on small organic molecules and then further extend our analysis and framework to tetrapeptides and protein monomers.
5.1 CONFORMER PRETRAINING
Datasets. We use GEOM-QM9 (Ramakrishnan et al., 2014) and GEOM-Drugs (Axelrod & Gomez- Bombarelli, 2022) following prior work in conformer generation (Xu et al., 2022; Ganea et al., 2021).

---

Published as a conference paper at ICLR 2026
Table 1: Performance Comparison on QM9 Unconditional Generation and Drugs Forward Simulation.
JSD (Mean
Median)
Method
Angle
Length
Torsion
TICA_0
TICA_0,1
MD ORACLE
0.042
0.028
0.032
0.031
0.192
0.134
0.318
0.291
0.413
0.394
AR EGNN
0.702
0.677
0.770
0,780
0.702
0.761
0.770
0.788
0.820
0.824
0.721
0.553
0.586
0.783
0.786
AR GEOTDM
0.752
0.746
0.699
0.694
0.466
0.506
0.456
0.463
0.714
0.719
GeOTDM
0.691
0.690
0.676
0.670
0.489
0.527
0.449
0.453
0.691
0.694
AGINTERROLATOR-SIIII
0.357
0.350
0.263
0.246
0.381
0.405
0.426
0.423
0.652
0.655
EGINTERPOLATOR-CAAE
0.292
0.363
0.642
MD ORACLE
0.036
0.023
0.030
0.028
0.215
0.131
0.484
0.494
0.610
0.630
AR EGNN
0.663
0.655
0.748
0.784
0.723
0.741
0.716
0.731
0.806
0.821
Drugs
0.765
0.745
0,526
0.791
0.795
AR GEOTDM
0.608
0.611
0.613
0.613
0.509
0.497
0.504
0.505
0.727
0.725
GEOTDM
0.640
0.645
0.643
0.645
0.498
0.505
0.531
0,550
0.712
0.720
EGINTERPOLATOR-SUNE SSMPLE
0.208
0.192
0.258
0.244
0.385
0.399
0.462
0.465
0.660
0.662
EGINTERPOLATOR-
0.1419
0.377
0.388
0.650
0.644
Our spatial model is pretrained separately on each dataset, using the same train/validation splits as (Xu et al., 2022) and a preprocessing pipeline similar to (Ganea et al., 2021) (Appendix B.1.1). This results in 37.7K/4.7K training/valiiaate 38.0K/4.8K training/validation molecules with 190.0K/23.7K conformers for Drugs. We then use the same test sets from (Xu et al.,, 2022; Shi al., 2021a), consisting of 200 distinct molecules, with 22.4K conformers for QM9 and 14.3K for Drugs.
molecules with /88.6K/23.75 7K conformers for QM9 and
Experimental Setup& & Baselines We train base BASICES model on this conformer generation task up to 800K steps for both QM9 and Drugs, learning 1000 denoising steps over only heavy atom coordinates. We compare the performance of our pretrained spatial models that reported in (Xu et al., 2022), namely GEODIFT-A as well as CONFGF (Shi et al., 2021a).
Metrics. Per prior work in the space, we utilize the Coverage and Matching metrics (Ganea et al., 2021; Xu et al., 2022) (Appendix B. B.1.3), We report both the Recall (R) to measure diversity and Precision (P) to measure accuracy. We use default Coverage values, 0.5A 1 1.25A (QM9/Drugs).
Results & Discussion. Results are summarized in Figure 3. Our pretrained BASICES model performs competitively with prior SOTA methods. For QM9, we prioritize precision-based metrics relevant to MD pretraining, which leads to slightly lower COV/MAT-R scores but superior fidelity in conformer bond angle and bond length distributions (see Appendix A.2).
5.2 MOLECULAR DYNAMICS FINETUNING
To generate MD data for diverse organic and drug-like molecules, we subsample from GEOM, resulting in 1 0009/101//200 crain/validation/ten splits for QM9 and 1 1137/1044/100 for Drugs. We then perform five, all-atom (including hydrogens), explicit-solvent simulations of 5 ns per molecule. In the test set, four trajectories are used as reference data and the fifth serves (MD OR Full simulation and force field details are provided in the Appendix B.2.
oracle baseline
Experimental Setup & Baselines. Unless otherwise noted, all models trained with trajectory time-steps A = 5.2 ps. We learn across heavy atoms and use 1000 denoising steps. We compare our EGINTERPOLATON framework against several representative approaches. First, we evaluate against GEOTDM (Han et al.. 2024), recent all-atom trajectory diffusion model. We also implement Markovian autoregressive baselines using EGNN (Hoogcboom al., 2022a) and the Equivariant Transformer (Thölke & Fabritíis, 2022) as push-forward networks, denoted AR + EGNN and AR + ET, respectively. Finally, inspired by dos Santos Costa et al. (2024), we include a autoregressive diffusion baseline that adopts GeoTDM's architecture, denoted AR + GEOTDM.
5.3 UNCONDITIONAL GENERATION
In the unconditional generation setting, train models to generate 2.6 ns trajectories with no reliance on a reference frame. For evaluation, we sample ten unconditional generations per molecule, resulting in 26 of generated trajectories. We focus QM9 for this setting given the smaller
7

---

Published as a conference paper at ICLR 2026
lofy
10
Sefeenes desToM
C:0.00
0-
Owm
lotsion ungle (tat)
18
18-2
10
E
F
1.0
1.0
SarSon
5
Sasgandees 6.-
Tarsinn
14
Torskon
0.00
2.0
0'0
Lag tine
1ag tine (n2
tine
Figure 4: (A) Bond length and (B) torsion angle distributions from reference (red), generations (green), and GeoTDM (blue). MSM occupancies from reference versus (C) our generations and (D) MD oracles. Autocorrelations of torsion angles for example molecule from (E) reference, (F) our generations, and (G) GeoTDM. Gray dashed line marks the 1/e decorrelation threshold.
memory footprint of these molecules. In Appendix A.5, we also highlight block diffusion roll-outs for 1560--Drugh in an unconditional manner.
Distributional & Energetic Results. A prerequisite to good molecular dynamics, evaluate similarity between generated and reference trajectories using average -hasnnnn divergence (ISD) across key collective variable distributions: bond lengths and angles (energetically constrained features), as well as torsions. As shown in Table 1, EGINTERPOLATON consistently outperforms baselines, with the CASC variant further improving over SIMPLE. Figure 4A,B examples illustrate gains over GeoTDM (Han et al., 2024), with near-perfect alignment to ground-trute -ruth bond-length distributions, closely matched tri-modal torsion profiles, and similar trends across additional collective variables in Figure 1. Moreover, important potential energy analyses are reported in Appendix A.7, E.5, where EGINTERPOLATOR shows markedly improved agreement over GEOTDM.
5.4 FORWARD SIMULATION
In the forward simulation setting, models are trained to generate 1.3 ns trajectories conditioned on reference frame. We then extend these to 5.2 ns using successive block diffiusion roll-outs, sampling five such trajectories per molecule. This setting focuses on GEOM-Drugs, targeting larger molecules.
Distributional Energetic Results. Across all metrics in Table I, EGINTERPPOLATOO outperforms baselines and approaches the distributional fidelity of the replicate MD ORACLE torsions We once again see that the CASC variant further improves SIMPLE. Additionally, complementary potential energy analyses, including quantifying error propagation in short (4-block) and long (16-block) diffusion roll-outs, are reported in Appendix A.7, E.5 and further support our methods.
Dynamical Results. Assessing the dynamical consistency of our model, Table 1 shows that method outperforms baselines and approaches the MD oracle in the distribution of the leading time-lagged independent component analysis (TICA) components, which capture the system's 's slow dynamics. We evaluate torsional dynamics via decorrelation time and find that EGINTERPOLATOR better captures distinct relaxation behaviors within molecules compared to GeoTDM (Fig. 4E.F.G). although certain fast relaxations seem to be a challenge. Furthermore, by constructing Markoy State Models (MSMs) from torsion angles and clustering into 10 metastates, we observe agreement in metastate occupancy between generated and reference trajectories (Fig. 4C). Our model even surpasses MD oracle baselines in capturing coarse-graines dynamical distributions (Fig. 4D).
5.5 INTERPOLATION
In the interpolation (or transition path sampling) task, models generate 0.52 ns trajectories condi- tioned on both start and end frames. As this setting requires endpoint conditioning, we compare only to the MI. baseline GeoTDM (Han al., 2024). Results are reported for Drugs (QM9 in Appendix
8

---

Published as a conference paper at ICLR 2026
A
PES (Naferenccl
State
State
State
State
State
State
300
270
100
0.5
10, 26
-.05
6o, mm
B
inforedation bujodarry
10, 0.0
90. m.
9.0
510
0.28
0.02
02-
8.01
MSK
Va ld path nate
Average path prob.
Valid parh prob.
Figure 5: (A) Reference free energy surface along the top two TICA components. (B) Generated interpolation trajectory projected onto the reference surface (red = start, orange end). Surface is colored by metastate assignment. (C) Key frames from intermediate metastates. (D) Statistics comparing JSD, valid path rate, average path probability, and valid path probability for generated trajectories and replicate MD oracles.
A.3), using the MSM pipeline from Jing et al. (2024c) to benchmark against MD oracles varying lengths. Given prior stronger empirical performance, we use the CASC variant for this task.
Evaluation. Following Jing et al. (2024c), we frame interpolation as transition path sampling. An MSM built from reference trajectories defines two distant metastates as start and end states, from which we sample 900 frame pairs. Our model generates 900 corresponding trajectories, evaluated against reference and MD oracles using JSD over metastate occupancies. Owing the high barrier and rare transitions, we also report valid path rate, average path probability, and valid path probability.
Results. As shown in Fig. 5D, our 0.52 ns trajectories yield the lowest JSD and highest average path probability, outperforming MD oracles of equal length and matching longer ones in path quality. Although long oracles achieve higher valid path rates, our model excels at generating high--robabillty valid transitions. Fig. 5A,B further show generated trajectory traversing key metastates on the reference FES, efficiently reaching the target end states.
5.6 ABLATION STUDY
We present main ablations here, with additional in Appendix A.8.
Table 2: Ablation on QM9 Unconditional Generation and Drugs Forward Simulation.
Median)(I)
Structural Pretraining. We evaluate trained
Method
Bond Angle
Bond Length
Torsion
TICA,,1
MOANTERROLATOO-NNIII without conformer pretraining. In Table 2, this yields degraded bond length, angle, torsion fidelity, and di- minished TICA 0,1.
Mean Median
Median
Mean
Median
Mcan
Median
Drugs QA9
EGINTERPOL ATOR-N
0.338
0.538
D.583
0.580
0,441
0.493
0.680
0.685
EGINTERPOLATOR
0.305
0.292
0.210
0.188
0.363
0.380
0.636
0.642
EGINTERPOLATEE
EGGNTTRPOI ATOR-N
0.332
0.332
D.386
0.383
0.455
0.465
0.698
0.703
EGINTERPOLATOR
0.173
0.153
0.142
0.112
0.377
0.388
0.650
0.644
Interpolation and Architecture EGINTERPOLATON CAAPPOOLLTO-SSAAAAAA removes (1) our cascaded layer design
and (2) interpolation, using a residual stack of temporal modules atop pretrained spatial layers as finetuned head. In Table 2, this variant underperforms EGINTERPOLATOR, underscoring the importance of our interpolation architecture.
5.7 TETRAPEPTIDES
We extend our evaluation to tetrapeptides using the Timewarp dataset (Klein et al., 2023), which comprises 1500/400/433 train/validationttst sequences simulated for up 50 (train) and 500 ns (validation/test) under all-atom smplicit-solvent MD. Models are trained with At 10 ps and generate 2.5 ns rollouts conditioned on reference frame, which are iteratively composed into 10

---

Published as a conference paper at ICLR 2026
A
ACKY
Timewarp Temrpeppide
Matrie (JSD)
GROTDM
Bond Angl (1)
0.182
0.607
Bond Leugth (1)
IU774
U1643
Tomden SCC.)
Topion BB
11,95
11.211
(1520)
0.554
GUOF A
Princte
Torsion
(L)
(2)
Rasidue
Guo!
Figure 6: (A) Free energy surface along top two TICA components for a reference (top), ours (top), and GeoTDM (bottom) letrapeptide trajectory. (B) Torsion auto-correlations from ours reference (left), ours (middle), and GeoTDM (right) (C) Key collective variable distribution JSD metrics. (D) C-a RMSF analysis and visualization for selected protein dynamics generation.
ns trajectories, with five samples per peptide. We compare EGINTERPOLATOR against GEOTDM, evaluating all methods against 50 ns reference simulations from the test set. As no conformer dataset exists for tetrapeptides, we construct one directly from the Timewarp training frames, detailed in Appendix B.1.1. This yields 1057/200 training and validation peptides (10.5K/2.7K conformers).
5.7.1 RESULTS
As shown in Figure 6C, method significantly lowers the JSD of both backbone and side-chain torsions relative to GeoTDM. This advantage is reflected in the free-energy landscapes (Figure 6A), where EGINTERPOLATOR exhibits sharper, better-resolved basins, while GeoTDM remains diffuse and unstructured. These gains also carry over to potential-energ metrics reported in Appendix A.7. Beyond per-frame frame fidelity, our model attains markedly improved dynamical consistency, achieving lower JSD in the leading TICA components and MSM occupancies (Figure 6C), as well as well- aligned de-correlation times (Figure 6B).
5.8 PROTEIN SIMULATION
We extend our framework to protein monomer dynamics using the ATLAS dataset (Meersche et al., 2024), training forward-simulation model and following the data splits of Jing al. (2024a). Building on Boltz1 (Wohlwend et al., 2024), we incorporate a temporal module- module-pair-biasee biir-biased sliding- window spatial attention, per Boltzl, combined with interleaved RoPE-based temporal attention layers (Su et al., 2023) across atoms/tokens-to enable trajectory generation. During training, we apply random rigid-body augmentations and superpose trajectories to zero-reference frame. Our experiments trained on 200 proteins, with 30/50 for validation/testing, generating 250-frame segments 100 ps and composing four such blocks for 100 ns rollouts. Preliminary results on the example protein from Jing et al. (2024b) are shown in Figure 6. Using 100 diffusion steps, generations take 0.12 (s) per frame.
CONCLUSION
We have introduced diffusion model for modeling MD distributions by pretraining structure model on conformer dataset and then finetuning on trajectory dataset. At the core of our approach is an module named EGINTERPOLATOR that mixes the output from the pretrained structure model and the temporal model to captures the temporal dependency. Our approach demonstrates strong performance in terms of producing realistic MD trajectories diverse benchmarks and tasks.
10

---

Published as a conference paper at ICLR 2026
ACKNOWLEDGMENT
We thank the anonymous reviewers for their feedback on improving the manuscript. This work was supported by ARO (W911NF-21-1-0125) ONR --00011----1-2159,, and the CZ Biohub.
REFERENCES
B. J. Alder and T. E. Wainwright. Studies in molecular dynamics. i. general method. The Journal of Chemical Physics, 31(2):459-44 August 1959. doi: 10.1063/1.173033 URL https: //doi. www.orrg///00 /t.rg/1..063/1111 /63/1.33... 00..1111.1..103766666 1730376.
Andrej Antalik, Andrea Levy, Sonata Kvedaravičiütt, Sophia K. Johnson, David
Bharath Raghavan, François Mouvet, Angela Acocella, Sambit Das, Vikram Gavini, Davide Mandelli, Emiliano Ippoliti, Simone Meloni, Paolo Carloni, Ursula Rothlisherger, and Jógvan Magnus Haugaard Olsen. Mimic: A high-performance framework for multiscale molecular dynamics simulations. The Journal of Chemical Physics, 161(2), July 2024, ISSN 1089-7690, doi: 10.1063/5.02110555 URL http: /xx doi. org 1063 0211053.
Simon Axelrod and Rafael Gomez-Bombanne Geom: for property prediction and molecular generation, 2022. URL https::/aaxxv..oort
molecular conformations
2006 6 05531. 3, 4,4,6
Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization, 2016. URL
https: / /ttp///avvv//////////ee////aella org/ aww.aabss/01 06450. 27
Christoph Bannwarth, Sebastian Ehlert, and Stefan Grimme. Gfn2-xtb-an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions. Journal of Chemical Theory and Computation, 15 (3):1652-1671, 2019, doi: 10.1021/acs.je Naoc.8801166 URL https: /tt///i..oo/o http:///oooooo..///2////222// acs jete. 8b01176. PMID: 30741547.
Helen M. Berman, John Westhrook, Zukang Feng, Gary Gilliland, Bhat, Helge Weissig, Ilya N. Shindyalov, and Philip E. Bourne. The protein data bank. Nucleic Acids Research, 28(1)2235-242, 01 2000. ISSN 0305-1048. doi: 10.1093/nar/28. 1.235. URL https: http://ti.ooo......//
Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models, 2023. URL https::////.mm /ttp///axvvv/.e///e//eee/eaa org. 02804
Simon Boothroyd, Pavan Kumar Behara, Owen C. Madin, David Hahn, Hyesu Jang, Vytautas Gapsys, Jeffrey R. Wagner, Joshua T. Horton, David L. Dotson, Matthew W. Thompson, Jessica Maat, Trevor Gokey, Lee-Ping Wang, Daniel J. Cole, Michael K. Gilson, John D. Chodera, Christopher I. Bayly, Michael R. Shirts, and David L. Mobley. Development and benchmarking of open force field 2.0.0: The sage small molecule force field. Journal of Chemical Theory and Computation, //doi. aooo.oorg/00.. 1021 accs. jetc. 3cC0039. PMID: 37167319. 23
2023. doi: 10. 11002//ac.jctt.330000
URL https:
Johannes Brandstetter, Rob Hesselink, Elise der Pol, Erik Bekkers, and Max Welling. Geometric and physical quantities improve e(3) equivariant message passing, 2022. URL
org/ abs 2110.0100000 02905.
Tim Brooks, Bill Peebles, Connor Holmes, Will DePue, Yufei Guo, Li Jing, David Schnurr, Joe Taylor, Troy Luhman, Eric Luhman, Clarence Ng, Ricky Wang, and Aditya Ramesh. Video generation models world simulators. 2024. URL https: pattpss//openatt /tpp///ppaa.////////// www.coooo/eeeeeeeeeee research/ simulators.
Hileo-geneeaan inneeerttiiiooiieoo moooomomdelsss -a--wssolldd -
Stefan Chmiela, Alexandre Tkatchenko, Huziel E Sauceda, Igor Poltavsky, Kristof T Schütt, and Klaus-Robert Müller. Machine learning of accurate meergyccoseervng molecular force fields.
Science advances, 3(5)ee603015 2017.

---

Published as a conference paper at ICLR 2026
Tom Darden, Darrin York, and Lee Pedersen. Particle mesh ewald: An n-log(n) method for ewald sums in large systems. The Journal of Chemical Physics, 98(1)):1089-100092 1993. ISSN 0021-9606. doi: 10.1063/1.464997.
Allan dos Santos Costa, Ila Mitnikov, Franco Pellegrini, Ameya Daigavane, Mario Geiger, Zhonglin Cao, Karsten Kreis, Tess Smidt, Emine Kucukbenli, and Joseph Jacobson. Equijump: Protein dynamics simulation via sequi-equvvariant stochastic interpolants, 2024. URL htw.t::///////m... //apps/////xvvv org/abs// 241 0. 09667.66667 3,7
Peter Eastman, Jason Swails, John D. Chodera, Robert T. McGibbon, Yutong Zhao, Kyle A. Beauchamp, Lee-Ping Wang, Andrew C. Simmonett, Matthew P. Harrigan, Chaya D. Stern, Rafal P. Wiewiora, Bernard R. Brooks, and Vijay S. Pande. Openmm 7: Rapid development of high performance algorithms for molecular dynamics. PLOS Computational Bioloy, 13(7):1-17, 07 2017. doi: 10. 137 /t3////ourall.c/ 1005659. URL :tttp:://6ol.org11..113333 jouruna pcbi 1005659. 23
Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, and Max Welling, Se(3)-tramsformer:: 3d roto- translation equivariant attention networks, 2020. URL https: /ttp://aaxvvvv.. www.:iiw.rg/ab//00000
10503.
Octavian-Eugee Ganea, Lagnajit Pattanaik, Connor W. Coley, Regina Barzilay, Klavs F. Jensen, William H. Green, and Tommi S. Jaakkola. Geomol: Torsional geometric generation of molecular 3d conformer ensembles, 2021. URL https: /ttp://aaavvv/aaeeeeeeeeeeawael/ org/ abs//106. 07802. 6, 22, 26
Xiang Gao, Farhad Ramezanghorbani, Olexandr Isayev, Justin S. Smith, and Adrian E. Roitberg. Torchani: A free and open source pytorch- based deep learning implementation of the ani neural network potentials. Journal of Chemical Information and Modeling, 60(7):3408-344 2020. doi: 10. 10.1/s// jeim.0c0000511 URL https: /ww.oo.ooooooooo www.:o.oooo.oooooooooooooooo 1021
022000211001 / acss jeim. 0c00451.
PMID: 32568524. 17
Jiaqi Han, Minkai Xu, Aaron Lou, Haotian Ye, and Stefano Ermon. Geometric trajectory diffusion models. arXiv preprint arXiv:2410. 10..24200..3.7. 2024. 3, 5, 7, 8, 19, 27, 28, 29
Jonathan Ho. Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020a.
Jonathan Ho. Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models, 2020b. URL https: /ppp://arxivv org/ abs 2006 11239. 23
Emiel Hoogeboom, Victor Garcia Satorras, Clément Vignac, and Max Welling. Equivariant diffusion for molecule generation 3d. In International conference on machine learning, pp. 8867-8887. PMLR, 2022a. 3.
Emiel Hoogeboom, Victor Garcia Satorras, Clément Vignac, and Max Welling. Equivariant diffusion for molecule generation in 3d, 2022b. URL https: //axxivv////xi....// http://a.i.gggaa..aa....... wwt/ab/////eooooccce/...ceeaaaee 220/3.20.. ..0.3.1..0000 17003. 2
Aapo Hyvärinen and Peter Dayan. Estimation of non-normalized statistical models by score matching.
Journal of Machine Learning Research, 6(4), 2005. 29
Bowen Jing, Stephan Eismann, Patricia Suriana, Raphael L.. Townshend, and Ron Dror. Learning from protein structure with geometric vector perceptrons, 2021. URL https: /taptt:::///xiiii /ttp/x.xxv.gg/////
abs/2009. 01411. 27
Bowen Jing, Bonnie Berger, and Tommi Jaakkola. Alphafold meets flow matching for generating protein ensembles. 2024a. URL https: puttps://ett //tpr//aaavi.///ia///a org/ abs/2402... 04845. 1, 10
Bowen Jing, Hannes Stärk, Tommi Jaakkola, and Bonnie Berger. Generative modeling of molecular dynamics trajectories. arXiv preprint arXiv:2409. /7808, 2024b. 10, 15,
Bowen Jing, Hannes Stärk, Tommi Jaakkola, and Bonnie Berger. Generative modeling molecular dynamics trajectories, 2024c. URL https: /tt.//iivvv/.//////// wwwp:/www///b///00/00000 17808. 1, 1,9, 25
12

---

Published as a conference paper at ICLR 2026
John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Zidek, Anna Potapenko, Alex Bridgland, Clemens Meyer, Simon A A Kohl, Andrew Ballard, Andrew Cowie, Bernardino Romera-Paredes, Stanislav Nikolov, Rishub Jain, Jonas Adler, Trevor Back, Stig Petersen, David Reiman, Ellen Clancy, Michal Zielinski, Martin Steinegger, Michalina Pacholska, Tamas Berghammer, Sebastian Bodenstein, David Silver, Oriol Vinyals, Andrew W Senior, Koray Kavukcuoglu, Pushmeet Kohli, and Demis Hassabis. Highly accurate protein structure prediction with AlphaFold. Nature, 596 (7873):583 589, 2021. doi: 10. (1588/41588-0021-03333
Wolfgang Kabsch. A solution for the best rotation to relate two sets of vectors, Acta Crystallographica Section A: Crystal Physics, Diffruction, Theoretical and General Crystallography, 32(5):922-923, 1976. 23, 28
Leon Klein, Andrew K. Foong, Tor Erlend Fjelde, Bruno Mlodozeniec, Mare Brockschmidt, Sebastian Nowozin, Frank Noé, and Ryota Tomioka. Timewarp: Transferable acceleration of molecular dynamics by learning time-coarsened dynamics, 2023. URL, https: /ttp:///axxvvvvv.ao abs/2302. 01 170. 1, 9, 23
Alessandro Laio and Michele Parrinello. Escaping free-energy minima. Proceedings of the National Academy Sciences, (2920)) 2002. doi: 10.1073/paas.22227339999 http:::: // //www. pnas org/ htlgg//di//e abo 10. 1073 / 2 2024273999
Daniel S. Levine, Muhammed Shuaibi, Evan Walter Clark Spotte- Michael G. Taylor, Muham- mad R. Hasyim, Kyle Michel, Ilyes Batatia, Gábor Csányi, Misko Dzamba, Peter Eastman, Nathan C. Frey, Xiang Fu, Vahe Gharakhanyan, Aditi S. Krishnapriyan, Joshua A. Rackers, San- jeev Raja, Ammar Rizvi, Andrew S. Rosen, Zachary Ulissi, Santiago Vargas, C. Lawrence Zitnick, Samuel M. Blau, and Brandon M. Wood. The open molecules 2025 (omol25) dataset, evaluations, and models, 2025. URL httpt:t///saatt //apxiv/////vvv/////a///: http://aaai..oogaa////////////// wtt.ooogg////oooo 2505. 08700876666 62. 3
Andrew McCammon, Bruce R. Gelin, and Martin Karplus. Dynamies of folded proteins. Nature, 267(5612):585 590, 1977. doi: 10.1038/267855a.
Alexandra Mclsaac, Pavan Kumar Behara, Trevor Gokey, Chapin Cavender, Joshua Horton, Lily Wang, Hyesu Jang, Jeffrey Wagner, Daniel Cole. Christopher Bayly, and David Mob- ley. wwtpr/eeeeeeeoooeeffffrrerfeeiee zenodo. 10533.. 23
January 2024. URL htattps://oi..orre 5281/
Yann Vander Meersche, Gabriel Cretin, Aria Gheeraert, Jean-Christophe Gelly, and Tatiana Galochk- ina. Atlas: protein flexibility description from atomistic molecular dynamics simulations. Nucleic Acids Research, 52(DI):D344-D39) 2024. doi: 10. 10.1a////ar/ 1084. 4, 10
Alex Morehead and Jianlin Cheng. Geometry-complete diffusion for 3d molecule generation and optimization, 2024. URL
/ 23322 04313. 2
Frank Noé, Simon Olsson, Jonas Köhler, and Hao Wu, Boltzmann generators sampling equilibrium states of many-body systems with deep learning, 2019, URL https: : //aaxxiivvoorg///aa abs/ 1812. 01929.
Jiwoong Park and Yang Shen. Equivariant blurring diffusion for hierarchical molecular conformer generation, 2024. URL https: aawiv.iiiiiv//iii//aaaaaaaaaavva org/ abs 2211 20255. 2
Saro Passaro, Gabriele Corso, Jeremy Wohlwend, Mateo Reveiz, Stephan Thaler, Vignesh Ram Somnath, Noah Getz, Tally Portnoi, Julien Roy, Hannes Stark, David Kwabi-Addo, Dominique Beaini, Tommi Jaakkola, and Regina Barzilay. Boltz-2: Towards accurate and efficient binding affinity prediction. bioRxiv, 2025. doi: 10. 201/2125 06. 14.659707. URL https: : //www. biorxiv.erg/come wwtp:/oot/otoeteeeeeee /ear 2025 / 06 18/ 8 2025. 06 14 659707.
Alexander S. Powers, Tianyu Lu, Rohan V. Koodli, Minkai Xu, Siyi Gu, Masha Karelina, and Ron O. Dror. Medsage: Bridging generative ai and medicinal chemistry for tructure-based design of small molecule drugs. bioRxiv, 2025. doi: 10.1101/2025.05. 10..6.53.......11..... URL https: 653100
//www.bi orxiv wwrg cowtent/eeaettiieeeee /ttmm///t/eerrr/////////////////
13

---

Published as a conference paper at ICLR 2026
A. Rahman. Correlations in the motion of atoms in liquid argon. Phys. Rev, 136:A405 A411, Oct 1964. doi: 10.1103//hysRev.l30..o 136.4405. URL https: prctps://linke http:///......a...o///////...... PhysRev. .A405.
Raghunathan Ramakrishnan, Pavlo O Dral, Matthias Rupp, and O Anatole von Lilienfeld. Quantum chemistry structures and properties of 134 kilo molecules. Scientific Data, 1, 2014. 4, 6
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High- resolution image synthesis with latent diffusion models. 2022 ieee. In CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10674-10685, 2021. 3
Victor Garcia Satorras, Emiel Hoogeboom, Fabian Bernd Fuchs, Ingmar Posner, and Max Welling. E(n) equivariant normalizing flows. A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, 2021a. URL https: / //openreview net wwwpeeennneeootttdndeeee/e. doooummiid-SSngnLoooli
3
Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. E(n) equivariant graph neural networks arXiv preprint arXiv:2102.09844, 2021b. 3, 6, 26, 28, 29
Martin K. Scherer, Benjamin Srendelkamp-Schroee Fabian Paul, Guillermo Strez-Hernández, Moritz Hoffmann, Nuria Plattner, Christoph Wehmeyer, Jan-Hendrik Prinz, and Frank Noé. Pyemma
Moritt
2: A software package for estimation, validation, and analysis of markov models. Journal of Chemical Theory and Computation, 11(11):5525-5544 2015. doi: 10.1021/acs.jct J03.500333 URL https: / / /doi..... wrg/ 100 1021/ /acs. jetc. 343. PMID: 26574340. 25
David E. Shaw, Ron O. Dror, John K. Salmon, J. P. Grossman, Kenneth M. Mackenzie, Joseph A. Bank, Cliff Young, Martin M. Deneroff, Brannon Batson, Kevin Bowers, Edmond Chow, Michael P. Eastwood, Douglas J. Ierardi, John L. Klepeis, Jeffrey S. Kuskin, Richard H. Larson, Kresten Lindorff-Larsen, Paul Maragakis, Mark A. Moraes, Stefano Piana, Yibing Shan, and Brian Towles. Millisecond-scale molecular dynamics simulations on anton. In Proceedings of the Conference on High Performance Computing Networking. Storage and Analysis, SC '09, New York, NY. USA, 2009. Association for Computing Machinery. ISBN 978 605587448. doi: 10.1145/1654059. 1654126.. URL https: : doi. org/ 1145 11541555555599 1654126. I
Chence Shi, Shitong Luo, Minkai Xu, and Jian Tang. Learning gradient fields for molecular conformation generation. In International conference on machine learning, pp. 9558-9568. PMLR, 2021a. 7, 22
Chence Shi, Shitong Luo, Minkai Xu, and Jian Tang. Learning gradient fields for molecular conformation generation, 2021b. URL https: http/aaxxvv//.////////////.atllt org/ abs/ 21w... 03902. 26
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference machine learning, pp. 2256-2265. PMLR, 2015. 3
Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019. 3, 28, 29
Yang Song, Jascha Sohl-Dickstein, Diederik Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021. URL htt.....tttttss//oeeeeeeeeeeeee http:///ppneeeeeeeeeeeeee http:/.weeeoorreeeeeeeeeeeeoeeee forum?
id=PxTIC12RRHS, 3, 28
Jianlin Su, Yu Lu, Shengfeng Pan, Ahmed Murtadha, Bo Wen, and Yunfeng Liu. Roformer: Enhanced transformer with rotary position embedding, 2023. URL 09864. 10
Philipp Thölke and Gianni De Fabritiis. Torchmd-net: Equivariant transformers for neural network
based molecular potentials, 2022. URL https: // //arxivvvvvv/////////////// .org/oorraaaao abs 2202..200200 02554.77.. 7, 28
Loup Verlet. Computer "experiments" classical fluids. i. thermodynamical properties of lennard- jones molecules. Phys. Rev., 159:98-103, Jul 1967. doi: 10. 1033//yysRe..155.90 URL https: //link. aps. wwtppppp.op.ooppppppppppoooooosp 03 /wt////hyrevv..e 159. 98.
14

---

Published as a conference paper at ICLR 2026
Jeremy Wohlwend, Gabriele Corso, Saro Passaro, Mateo Reveiz, Ken Leidal, Wojtek Swider- ski, Tally Portnoi, Itamar Chimn, Jacob Silterra, Tommi Jaakkola, and Regina Barzilay, Boltz-
I: Democratizing biomolecular interaction modeling. bioRxiv, 2024. doi: 10.1101/2024.11 19.624167. URL https::: http://wwwwwwoooote/ www.biiowiivv...o...o...o..w 11. 11.19. 6244 67. Preprint. 10
Can Xu, Haosen Wang, Weigang Wang, Pengfei Zheng, and Hongyang Chen. Geometric-facilitate denoising diffusion model for 3d molecule generation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 338-346, 2024a. 2
Minkai Xu, Lantao Yu, Yang Song. Chence Shi, Stefano Ermon, and Jian Tang. Geodiff: A geometric diffuuion model for molecular conformation generation. In International Conference on Learning Representations, 2022. URL https: httpsss///ppeevveeeee net/ forum? www.:idddd...eeaeeee 3, 6, 7, 22, 23, 27
Minkai Xu, Alexander Powers, Ron Dror, Stefano Ermon, and Jure Leskovec. Geometric latent diffusion models for 3d molecule generation. In International Conference on Machine Learning. PMLR, 2023. 2, 3
Minkai Xu, Jiaqi Han, Aaron Lou, Jean Kossaifi, Arvind Ramanathan, Kamyar Azizzadenesheli, Jure Leskovec, Stefano Ermon, and Anima Anandkumar. Equivariant graph neural operator for modeling 3d dynamics. In Forty-first International Conference on Machine Learning, 2024b. URL https: hwtp//eeeeeeeeeeeeeeeee/ee...wwe .nt/ MorrumiddddccRCmmee
Zhijum Zhang, Xinzijian Liu, Kangyu Yan, Mark E. Tuckerman, and Jian Liu. Unified efficient thermostat scheme for the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics. The Journal of Physical Chemistry A, 123(28):6056-600) 6079, 2019. doi: 10. 10.1cs//acs.jpp http:/acssjcpc..... jpca.9b02771. URL https::/ /doi http:://dooooooo///o// C21 /acs. jpca. 9b02771. PMID: 31117592. 24
A EXPERIMENTS CONTINUED
A.1 COMPARISON TO MDGEN THE TETRAPEPTIDE DATASET
We benchmark our model against MDGen (Jing al., 2024b), which parameterizes tetrapeptide conformations explicitly through backbone and sidechain torsional angles. Using the subsampling procedure described in Appendix B.1.I, convert MDGen training trajectories into peptide conformer dataset and augment with a pruned Time Warp-derived conformer set to avoid data leakage. We then fine-tune conformer model on this combined dataset, initializing from GEOM- DRUGS pretrained weights. As shown in Table 3, our downstream peptide EGINTERPOL preserves fine- fine-grained structural information and superior fidelity in bond lengths and bond angles, which are essential for accurate all-heavy-atom molecular dynamics and modeling small molecules. However, it underperforms MDGen on torsional distributions and torsion-derived dynamical metrics. This gap suggests that MDGen's 's pasionn-enttre representation confers an advantage in capturing peptide rotational behavior, where our model's strengths are geometric consistency at an atomic level.
A.2 OPTIMIZING FOR CONFORMER PRECISION METRICS
As discussed in Section 5.1, 1, we prioritize precision-based conformer quality metrics when selecting our base structure model. While this may come the cost of lower COV/MAT-R scores, we observe superior fidelity in bond length, bond angle, and torsion angle distributions aspect consider more critical for a pretrained structure module.
We highlight this point using two checkpoints of the BASICES model trained QM9. In Table 4 we can see that while 539 lacks in COV-R, R, it does substantially better than 99 in COV/MAT-P metrics. In Figure 10, then see that 539 reflects high quality bond angle, length, and torsion distributions, as compared to 99. We select checkpoint 539 for the conformer results reported in Section 5.1 and for training the downstream trajectory models.
15

---

Published as a conference paper at ICLR 2026
Table 3: Results on MDGen Tetrapeptide Dataset
Metries (JSD)
EGINTERPOLAATOR
MDGEN
Bond Angle ({)
0.092
N/A
Bond Length (L)
0.056
N/A
Torsion BB
0.378
0.130
Torsion SC (L)
0.189
0.093
Torsion All (1)
0,265
0.109
TICAa (L)
0.409
0.230
TICAo1 (L)
0.568
0.316
MSM (1)
0.312
0.235
Table 4: Conformer metries on QM9 compared between two checkpoints.
Checkpoint
COV-R
f
MAT-R (A)
COV-P (%) f
MAT-P (Å) 4
Mean
Med.
Mcan
Med.
Mcan
Med.
Mcan
Med.
99
90.18
94.59
0.2969
0.3049
55.23
51.36
0,4932
0,4823
539
87.62
92.03
0.2574
0.2613
58.12
53.24
0.4451
0.4445
A.3
QM9 INTERPOLATION
QM9 Interpolation Statistics
0,55,
0.025
0.7
ND. 2.0 ns
0.6
MD. 1.0 ns
0.020
MD, 0.26 ms
0.015
0.4
0.3
0.010
0.005
0.1
0.0
0.000
MSM JSD
Valid path rate
Average path prob.
Valid path prob.
Figure 7: Statistics evaluating the JSD with the reference trajectories, valid path rate, average path probability, and valid path probability of generated trajectories and replicate MD oracles.
For the interpolation task on QM9 dataset, shown in Figure our 0.52 trajectories from CAsC consistently achieve the lowest probability, outperforming MD) oracles of the same duration. It reveals that method can samples transition paths between far metastates more efficiently. While the MD oracles exhibit higher valid path rates in this setting, model still performs competitively in generating high-probability valid transitions.
Shannon Divergence (JSD) and the highest average path
Figure 14 illustrates several free energy surfaces (FES) and corresponding metastate assignments for representative molecules. We observe that the generated trajectories successfully traverse key intermediate states and reach the appropriate end states, demonstrating the model's ability to perform efficient and meaningful transition path sampling.
A.4 DRUGS UNCONDITIONAL GENERATION
Since the molecules the Drugs dataset are more challenging systems than those in QM9, we further ablate the reliance the starting reference frame by conducting unconditional generation
16

---

Published as a conference paper at ICLR 2026
Table 5: Performance comparison on Drugs Forward Simulation versus Unconditional Generation.
Reported values are JSD (Mean - Median) 4.
Method
Bond Angle
Bond Length
Torsion
TICAo
TICA.,
GEOTDM
0.640 0.645
0.643 0.645
0.498 0.503
0.531 0.550
0.712 0.720
EGINTERFOLATOR-SIAE SIMPLE
0.208 0.192
0,258 0.244
0.385 0.399
0,462 0.465
0.660 0.662
SAANTEERROLATRR-AAAR.
0.173 0.153
0.142 0.112
0.377 0.388
0.454 0,441
0,650 0.644
EGINTERPOLATOR-CASE
0.220 0.202
0.195 0.168
0.414 0.429
0.499 0.496
0.689 0.697
experiment (U). Specifically, we retain the same experimental set-up but remove conditioning of the first block ground-trute -ruth frame, and retrain new unconditional generation model. As shown in Table 5, while performance does not match our EGINTERPOL. ATORR-O--OO CASC trained with forward simulation, the unconditional variant still surpasses GEOTDM trained with forward simulation by significant margin in terms of bond angle, bond length, and torsion distribution fidelity.
A.5 DRUGS LONG SIMULATION
To more rigorously evaluate generation quality, we repeat the forward-simulation experiments on DRUGS using long 16-block roll-out of 20.8 ns, generating one trajectory per molecule. Although this extended roll-out exhibits some degradation relative to the parallelized version-likely due to accumulated error propagation quantified in Section A.7-out our method still outperforms all baselines, including their parallel 4-block configurations, shown in Table 6.
A.6 MULTITASK/MODAI LEARNING
To further demonstrate our framework's s ability to generalize across molecular dynamics regimes, we first pre-train conformer model and then train dynamics interpolator jointly on QM9 and DRUGs for both forward simulation and unconditional generation. We benchmark this unified model against single-task counterparts on each dataset. As shown in Table 6, the unified model consistently outperforms all baselines, and notably achieves improved performance pretraining on more diverse and chemically complex systems can enhance dynamics generation quality even previously unseen molecules.
indiicain that
Table 6: Additional Performance Comparisons on QM9 Unconditional Generation and Drugs Forward Simulation.
JSD (Mean
Median) (1)
Method
Bond Angle
Bond Length
Torsion
TICAa
TICAuu
MD ORACLE
0.042
0.028
0.032
0.031
0.192
0.134
0.318
0.291
0.413
0.394
QMP
GROTDM
0.691
0.690
0.676
0.670
0.489
0.527
0.449
0.453
0.691
0.694
EGINTERPOLATOR
0.305
0.210
0.363
0.642
EGINTERPOLATORE
0.231
0.168
0.348
0.367
0.390
0.631
MD ORACLE
0.036
0.023
0.030
0.028
0.215
0.131
0.484
0.494
0.610
0.630
Drugs
GEOTDM
0.640
0.645
0.643
0.645
0.498
0.503
0.531
0.550
0.712
0.720
EGINTERPOLATOR
0.173
0,153
0.142
0,112
0.377
0,388
0.454
0,441
0.650
0.644
EGINTERPOLATOR--EE
0.212
0.197
0.216
0.195
0.417
0.434
0.488
0.506
0.681
0.679
EGINTERRPOLATOR-LONGG
0.680
A.7 ENERGY-BASEE ANALYSIS
In addition to evaluating collective variable distributions and MSM metrics as measures of trajectory fidelity, we further assess model rigor by examining the energy profiles generated trajectories. Per-frame energies
estimated using TorchANI2x (Gao et al., 2020) and reported in Hartrees. Alongside the results presented in this section, we also provide energy comparisons to ground truth trajectories for representative molecules from both datasets in Table 17.
17

---

Published as a conference paper at ICLR 2026
Table 7: Top: Average Wasserstein-1 (WI) distance between predicted and ground-truth (GT) energy profiles for EGINTERPOLATOR CASC and GEOTDM across dataset test sets. Bottom: Per-block WI analysis in forward simulation roll-outs for Drugs.
Dataset
EGInterpolator vs W1 GeoTDM vs GT W1
QM9
0.8127
2.9201
Drugs
0.7728
12.7664
Block
EGInterpolator vs GT W1
GeoTDM vs GT WI
0,2454
11.2398
0,3654
12.8999
0.3656
13 13.0270
0.3702
13. 13.1235
Table 8: Top: Average Wasserstein-1 (W1) distance between predicted and ground-truth (GT) energy profiles for EGINTERPOLATOR and GEOTDM across tetrapeptides. Bottom: Per-block W1 analysis of forward simulation roll-outs.
Metrie
EGINTERPOLATOR vs 4
Overall Energy W1 GEOTDM Energy W1
0.3806
12.8636
Block
2
3
4
EGINTERPOLATOR
0.2638
0.3912
0.4196
0.4494
GEOTDM WI
12.4955
12.9417
13.0007
13.0681
A.7.1 OVERALL RESULTS
In Table 8, we report the Wasserstein-11 (WI) distance between the energy distributions of generated trajectories and the ground-truth (GT) trajectories, averaged across the test sets of all datasets. Our framework achieves substantially lower WI distances than the GEOTDM baseline, demonstrating much closer correspondence to the GT energy profiles.
A.7.2 BLOCK DIFFUSION DETERIORATION
In Tables and 8, we address central concern forward roll-outs using block diffusion: the potential for еттог accumulation and degradation in sample fidelity over time. To quantify this, we conduct block-wise analysis of the generated trajectories and observe that our framework remains well aligned with ground-truth energy distributions, exhibiting only mild deterioration most notably between Blocks and 2. Extending this analysis to longer roll-outs, we find that unlike GeoTDM, our model does not collapse to degenerate energy states, though errors begin to compound beyond approximately frames. Mitigating this effect a promising direction for future work, where incorporating force or energy-based guidance during training inference may further improve Long-horizon stability.
A.8 TRAJECTORY MODEL ABLATIONS
A.8.1 FROZEN BASICES
As mentioned in Section 5.6, assess the benefit of fine-tuning the frozen spatial encoder by training fully end-to-end version of EGINTERPOLATOR, called EGINTERPOLATOR on the Drugs forward simulation task. In Figure 8, that performance remains largely unchanged across metrics, indicating that the pretrained spatial model generalizes well without task-specific tuning, while the temporal layers effectively capture the necessary dynamic information.
18

---

Published as a conference paper at ICLR 2026
Table wloek-wise Wasserstein-1 Progression. Mean WI error across 250-frame blocks during forward simulation.
Block
Frame Range
Mean W1 (4)
1-250
0.2303
2
251-500
0.2778
3
501-750
0.3693
4
751-1000
0.2769
5
1001-1250
0.4541
6
1251-1500
0.3962
7
1501-1750
0,3830
8
1751-2000
0.3805
9
2001-2250
0.5765
2251-2500 10
0.5861
2501-2750
0.6666
12
2751-3000
0.3979
13
3001-3250
0.4276
3251-3500
0.5328
15
3501-3750
0.4830
16
3751-4000
0.5192
Temporal Region
Mean W1 (L)
Early (Blocks 1-4; Frames 1-1000)
0.3460
Mid (Blocks 5-12; Frames 1001-3000)
0.5568
Late (Blocks 13-16; Frames 3001-4000)
0.4906
A.8.2 GENERALIZATION TO AN EXTENDED TEST SET
To further assess the robustness of our QM9 unconditional generation model, we evaluate performance on an extended test set of 959 molecules, which includes the original test set from Section 5.2. As shown in Table 10, we compare GEOTDM (Han et al., 2024), EGINTERPOLATOR-Y (without structure pretraining), and our full EGINTERPOLATON model. While all models perform comparably on this larger evaluation set, EGINTERPOLATON consistently outperforms the baselines, underscoring its strong generalization and the value of structural pretraining.
JSD Metrics by Category
EGinterpolater (Mean)
0.8
EGinterpolater (Median)
EGinterpolator (Mesn)
0.7
EGInterpolatee- (Median)
0.6
0.5
Score
0.4
0.3
Bond Angle
Bond Length
Torsion
Decorrelation
Figure 8: JSD metrics computed for Bond Angles, Bond Lengths, Torsions, and Decorrelation Times. Compared between EGINTERPOLATOR (green) and EGINTERPOLAAORR (purple).
19

---

Published as a conference paper at ICLR 2026
Table 11: JSD metries for bond angle, bond length, and torsion across QM9 and DRUGS datasets with and without temporal layers.
Model
Bond Angle (1)
Bond Length (4)
Torsion (1)
EGINTERPOLATOR NORMAL (QM9)
0.305 0.292
0.210 0.188
0.363 0.380
EGINTERPOLATOR 1 (QM9)
0.398 0.391
0.618 0.613
0.358 / 0.372
EGINTERPOL NORMAL (DRUGS)
0.173 0.153
0.142 / 0.112
0.377 / 0.388
EGINTERPOL a = (DRUGS)
0.435 0.445
0.580 0.091
0.378 0.382
Table 10: JSD Metric (4) for QM9 Unconditional Generation. Top: Trained on Standard Train,
evaluated on Enlarged Test. Bottom: Trained on Enlarged Train, evaluated on Standard Test.
Train Test
Method
Angle
Boad Length
Tonsion
TICA
TICA
Mean
Med.
Mcan
Mod.
Mean
Med.
Mean
Med.
Mean
GROTDM
0.690
0.690
0.674
0.668
0.488
0.529
0.452
0.451
0.695
0.699
Standard Enlarged
EGINTERPOLATOR
0.539
0.538
0,584
0.582
0.447
0.492
0.438
0.440
0.678
0.685
EGINTERPOLATOR
0.307
0.293
0.214
0.194
0.361
0.385
0.416
0.409
GROTDM
0.757
0.757
0.782
0.793
0.488
0.533
0.454
0.453
0.697
0.703
Enlarged + Standard EGINTERPOLATOR.N
0.470
0.460
0.540
0.544
0.433
0.481
0.443
0.440
0.681
0.691
EGINTERPOLATOR
0.296
0.286
0.361
0.247
0.370
0.388
0.405
0.394
0.636
0.638
A.8.3 CONTRIBUTION OF EXTENDED TRAIN SET
While our framework is motivated by the scarcity of trajectory data, we also evaluate model per- formance under increased supervision. We train on an enlarged dataset- 4x larger than the orig- inal comp-ssng 4437 molecules, with the original split from Section 5.2 as subset. As shown in Table 10, while EGINTERPOLATON substantially with more data, the latter maintains a clear advantage. This highlights the continued value of structural pretraining even in higher-data regimes.
and EGINTERPOLAATON interestingly do not improve
A.8.4 CONTRIBUTIONS OF THE TEMPORAL MODULE TO NON-TRIVIAL DYNAMICS
To assess the contribution of our temporal module in learning non-trivial dynamics specifically the fast torsional processes observed organic small molecules-we compare our framework run with and without the temporal component. We generate trajectories for both QM9 and Drugs with = 1 (i.i.d. conformers, i.e., no temporal interpolation). Additionally, we shuffle the frames both GT trajectories and our original model generations to establish baselines corresponding random frame orderings. We then computed torsional decorrelation times for conditions. While our method does not fully match GT torsional decorrelation times QM9, ps baseline (the MD frame rate). This supports that the temporal module learns non-trivial dynamical properties essential for modeling diverse molecule dynamics.
that it clearly avoids the trivial 5.2
A.8.5 CONTRIBUTION OF THE TEMPORAL MODULE TO STRUCTURE LEARNING
To asses if our temporal module's 's spatial update layers refine structural predictions during trajectory generation, we compare the collective variable JSD distributions between the normal and a = setting. As demonstrated in Table 11, the full interpolator improves bond lengths, bond angles, and torsions, indicating that the system can correct imperfections the conformer prior rather than inherit them.
A.9 a MIXING PARAMETERS: INTERPRETATION CONTRIBUTION
A.9.1 EMPIRICALLY LEARNED VALUES
We analyze the ranges of alpha values learned during training and in order to identify consistent patterns and interpretable behaviors in Figure and Figures 16, 17. As context: (1) Positive alpha values assign greater weight to the pretrained spatial model, while negative values emphasize the
20

---

Published as a conference paper at ICLR 2026
Table 12:
Mean torsional decorrelation times (ps) across test sets, comparing GT MD data, our original generations, i.i.d. conformer generations (a 1), and shuffled variants. Shuffled data collapse to the frame of 5.2 ps, reflecting lack of temporal structure.
Dataset
GT MD
Original Gen.
a Gen.
Shuffled GT
Shuffled Gen.
QM9 Test
101.0
13.59
5.2
5.2
5.2
Drugs Test
130.1
185.64
5.2
5.2
5.2
Logt Valuen per layer for Alpha Parmmeieess DestereAALL:
deviber Mit
desiar METUUUU
Logi.Valuss Values per layor for Alpha Panamotirrs
4.43
415
113
411
Figure 9: Top: Logits of for each spatial and temporal layer after convergence the QM9 uncon- ditional generation task, Bottom: Logits of a for each spatial and temporal layer after convergence on the DRUGS forward simulation task. Both: Results obtained with EGINTERPOLATOR -AAC..
temporal component; (2) alpha h/x correspond the pretrained spatial layer and the spatial layer in the temporal module, where h and x denote mixing coefficients for invariant and vector features, respectively; (3) Layer 5 does include an alpha h.t term, as this output is never used.
Overall, alpha values generally fall within [-0.25, 0.25). From Figure 9, we observe some exciting trends: in the first temporal block (alpha_x_t) and spatial block (alpha_x_s) of the temporal module, earlier layers prefer pretrained information, while later layers favor temporal module information. For the final temporal block (alpha 2), the model generally relies on newly trained information across layers. This supports our design choices: early layers focus structural integrity, while later layers prioritize dynamics, with the last temporal block reinforcing dynamic updates.
A.9.2 CONTRIBUTION TO CONFORMER GENERATION
Although the endpoints 0 and yield straightforward and well-defined inference dynamics, we also investigate the inference-ting time flexibility of this parameter by running EGINTERPOLATON as conformer generator QM9 while perturbing Specifically, linearly interpolate the mixing
21

---

Published as a conference paper at ICLR 2026
Table 13: QM9 results across for CASC and SIMPLE.
COV-R (%)
MAT-R (Å)
COV-P (%)
MAT-P (Å)
Mean
Med.
Mean
Med.
Mean
Med.
Mean
Med.
Casc
0.000
87.99
91.98
0.2539
0.2600
58.30
53.62
0.44.00
0.4397
0.025
87.82
92.98
0.2570
0.2598
57.70
53.17
0.4470
0.4396
0.050
88.34
92.84
0.2568
0.2556
58.29
53.78
0.4460
0.4439
0.075
88,16
93.61
0.2577
0.2610
57.38
52.86
0.4490
0.4467
0.100
88.47
92.66
0.2588
0.2654
57.14
52.51
0.4531
0.4523
0,125
89.09
94.36
0.2579
0.2589
56.67
52.21
0.4581
0,4549
0.150
89.55
93.39
0.2580
0.2637
56.37
50.83
0.4618
0.4580
0.175
89.06
94.46
0,2621
0.2612
55.88
51.06
0.46669
0,4670
0,200
89.27
94.56
0.2633
0.2604
55.23
50.95
0.4697
0.4653
SIMPLE
0.000
88.11
92.47
0.2557
0.2553
59.03
54.52
0.4413
0,4439
0.025
88.54
91.28
0.2546
0.2540
58.27
53.72
0.4472
0.4419
0.050
89.71
94.13
0,2518
0.2577
58.20
54.24
0.4492
0.4397
0.075
90.34
94.20
0.2536
0.2589
57.79
53.51
0.4539
0.4496
0.100
91.11
95.36
0.2542
0.2589
57.14
52.23
0.4598
0.4542
0.125
92.11
96.36
0,2558
0.2638
57.19
53.04
0.4647
0,4582
0.150
92.05
96.07
0,2618
0.2665
57.14
54.30
0.4681
0.4630
0.175
92.21
96.39
0,2678
0.2737
55.58
51.75
0.4795
0,4675
0.200
92.63
96.08
0,2713
0.2783
54.94
50.63
0.4885
0.4850
GeoDiff-A
90.54
94.61
0.2104
0.2021
52.35
50.10
0.4539
0.4399
parameter logits between and the learned value a* by introducing a new variable [0, 1]. such that a' Aa X).
Across both the SIMPLE and CASC variants, we observe a trade-off between precision and diversity metrics summarized in Table 13. Notably, varying À allows recover and surpass the COV-R di- versity scores reported by GeoDiff. The SIMPLE variant exhibits a more favorable precision-diventie trade-off curve with respect X, which attribute to its closer alignment with theoretical formulation in Theorem 1. J. More broadly, these findings indicate that the temporal module captures aspects of conformational diversity beyond those provided the pretrained conformer model, and that the a parameters offer natural mechanism for controlling the balance between precision and conformational dynamics in the generated trajectories.
B EXPERIMENTAL DETAILS
B.1 CONFORMER PRETRAINING
B.1.1 DATA PREPROCESSING
The datasets obtained from the (Xu et al., 2022; Shi et al., 2021a) codebase are provided as pickle files, each containing list of PyTorch Geometric data objects representing individual conformers. We apply the following filtering steps to ensure data quality. First, we verify that the saved RDMol objects can be successfully sanitized using RDKit. Next, we remove any conformers exhibiting fragmentation in their RDMol representations. Following Ganea et al. (2021), we also account for conformers that may have reacted in the original data generation process. Namely, we compare the canonical SMILES strings derived from both the saved SMILES and the corresponding RDMo 1, and discard any conformers where the two do not match. We also exclude any molecules whose saved SMILES MIL cannot be converted into valid RDMel 1 by RDKit. Lastly, specific to method,
22

---

Published as a conference paper at ICLR 2026
remove hydrogens from the molecules according rdkit. Chem. Chem.Removell RemoveHs and retain heavy atoms. For QM9, this leaves [C. N. O, F). For Drugs, we have [C, N. O, P. CI, Br, 1, B, Si].
For each peptide in the Timewarp and MDen train/validation sets (Klein al., 2023) (Jing et al., 2024b), we compute per-residue o/v² dihedral features, subsample up to 10,000 frames, cluster them in dihedral space using K- K-medoids, and select the lowest-energy member of each cluster representative conformer, yielding 10 / 20 conformers per peptide.
B.1.2 TRAINING DETAILS
We train both the QM9, Drugs, and Tetrapeptide conformer models using 4 NVIDIA RTX A4000 GPUs, with an effective batch size of 128 (32 samples per GPU) and a learning rate x 10 10-4 Training is carried out until convergence, typically around 800K steps. As described in Section 5.1, all models are trained using 1000 diffusion steps. We adopt a DDPM framework (Ho et al., 2020b) with linear noise schedule. Additionally, employ equivariant loss function that leverages optimal Kabsch alignment (Kabsch, 1976), with more details in Section C.4.
B.1.3 EVALUATION DETAILS
We evaluate the quality of generated conformers using Coverage (COV-P) and Matching (MAT-P), both based on the root mean square deviation (RMSD) computed after Kabsch alignment (Kabsch, 1976).
Let Sg and S, denote the sets of generated and reference conformers, respectively. The metrics are defined
S,) = |55 C E Sq
min RMSD(C, 50 CES.
(6)
,A, [S,] OES,
min RMSD(C,C)) CES,
where 5 is a predefined threshold. COV-R and MAT-R, inspired by Recall, are defined analogously by swapping Sg and Sp..
Following Xu et al. (2022), we set [S, x |S, per molecule. The results reported in Section 5.1 correspond to the average COV=*/MAT=* scores across all test molecules. COV-P reflects precision by measuring the fraction of generated conformers that are sufficiently close to the reference set (within threshold 6), while MAT-P captures the mean deviation of each generated conformer from its closest reference match. High COV and low MAT scores indicate greater fidelity and precision in conformer generation.
B.2 MOLECULAR DYNAMICS FOR SMALL MOLECULES
B.2.1 PARAMETERIZZATION
We all-atom molecular dynamics simulations, including hydrogens, using OpenMM (Eastman et al., 2017) and employ openmmfrrce ields to apply small molecule force field parameter- izations developed by the Open Force Field Initiative (OpenFF) (Boothroyd et al., 2023). We follow the setup guidelines provided in the openmmforce fields GitHub repository. Specifi- cally, we adopt the o f-2 (Sage) (Melsaac al., 2024) small molecule force field in conjunction with base amber/protein.ccm fttp:/prr................. xml protein force field and combination of amber r/ /t tiippp.ptaaattt solvent and ion parameters. Continuing with standard hyperparameters, we set the nonbonded cutoff to 0.9 nm and the switch distance to 0.8 nm. Hydrogen mass repartitioning (HMR) is applied with a mass of 1.5 amu, along with constraints all hydrogen bonds. Long-range electrostatic interactions are computed using the Particle Mesh Ewald (PME) method under periodic boundary conditions. A padding of 1.5 nm is used for the explicit solvent box.
xm1 and amber ptaiberrtiiip_.t. 3p wtt.eHE..lliiaaaa..amaa
xml for explicit
Note that RemoveHs does not eliminate all hydrogen atoms and may retain chemically relevant ones (see the RDKit documentation). Our method explicitly incorporates and models such retained hydrogens.
23

---

Published as a conference paper at ICLR 2026
B.2.2 SIMULATION
All molecular dynamics simulations are performed using a friction coefficient ps temperature of 300 K, and an integration timestep of 4 fs. employing the LangevinMin MiMiiddee eelllennttgattt (Zhang et al., 2019). As described in Section 5.2, five independent trajectories are generated per molecule, each initialized from a conformer assigned to that molecule in the selected data subset. Each trajectory simulation begins with energy minimization, followed by 5000 steps of equilibration under constant volume and temperature (NVT) conditions. This is followed by a 4.5 production under constant pressure and temperature (NPT) conditions, comprising total of 1 1.25M integration steps. Trajectory simulation parallelized across 32 NVIDIA RTX A4000 GPUs and saved with frame rate of 400 fs/0.4 ps.
B.3 TRAJECTORY FINETUNING
B.3.1 DATASET PREPARATION
As mentioned in Section 5.2, we randomly sample subset of the molecules from the GEOM-QM9 and Drugs conformer data generate trajectory data from. As this is quite costly, for Drugs we generate simulations for the standard train/validation// we generate data for enlarged train/test sets along with the standard validation set. We then subsample 25% of the enlarged splits to be the standard train/test sets. A summary of the dataset splits is provided below:
splits mentioned in Section 5.2. For QM9,
Drugs:
Standard splits: 1137/1044/100 train/validdaioontess molecules
(5682/5209/ 96 associated trajectories)
QM9:
Standard splits: 1109/1018/ /240 train/validation/test molecules
(5534/5080/11) /1/9 associated trajectories)
Enlarged sets: 1437/955 train/test molecules (29132/4793 associated trajectories)
As note, of the test trajectories, we select baseline. Moreover, we filter out any molecules over 60 atoms in the Drugs dataset to reduce memory usage variance. Finally, the test for the interpolation is a subset of the standard test sets mentioned above. We further define this process of selection in Section B.6 and B.3.3.
of 5 per molecule be the MD ORACLE
B.3.2 TRAINING PROTOCOL
While the compute setup and batch size vary across datasets and generation settings, we consistently employ a DDPM framework with linear noise schedule and train all models using 1000 diffusion steps. A fixed learning rate of 10-4 is used and training is performed until convergence. Additionally, we adopt an equivariant loss function based on optimal global Kabsch alignment of trajectories, detailed in Section C.4. Setting-specifie training configurations provided in Sections B.4-B.6.
B.3.3 EVALUATION METRICS
Jensen-Shannon Divergence. We compute the JSD as implemented in scipy, where m (p + g)/2:
D(p m) + D(g m)
2
Torsions: The ID JSD is computed over a 100-bin histogram discretized across [-TT, x]. Bond Angles: The ID JSD computed over a 100-bin histogram discretized across [o, mr.
Bond Lengths: The ID JSD is computed over a 100-bin histogram discretized across
(100, 220) pm.
24

---

Published as a conference paper at ICLR 2026
Torsion decorrelation: The ID JSD is computed over 275-bin histogram discretized across [5, 1380] ps, which are corresponding to the minimum and maximum torsion decorrelation time of molecules across the dataset.
TICA-O and TICA-0,1: We reduce the dimensionality of the trajectory by time-lagged independent component analysis (TICA). Then ID, 2D JSDs are computed over 100-bin histograms on the first TICA component (TICA-0) and the first two components (TICA-0,1), respectively. Since different molecules have totally different TICA projections and values, we use the minimum and maximum values from each molecule as its unique discretization range for TICA-O and TICA-0,1. We use 10.4 ps (2 steps) lag time for QM9 and 20.8 ps (4 steps) for drugs.
Markov State Models. We intensively use Markov State Models (MSM) for interpolation tasks. We featurize reference trajectories with all torsion angles except for those within an aromatic ring. Then TICA is performed on the torsion-based trajectories. After dimensionality reduction, a k-means clustering algorithm is used to discretize the trajectories to 100 clusters. An MSM analysis is performed the trajectories of 100 states and PCCA+ spectral clustering from PYEMMA package (Scherer et al., 2015) is used to aggregate clusters to 10 coarse metastates. A second MSM analysis is done on the coarse trajectories. We use 52 ps (10 steps) lag time for QM9 and 104 ps (20 steps) for drugs.
To sample the start and end frames used in the interpolation task, we compute the flux matrix over the 10 metastates. To construct a high barrier and rare transition probability, we choose the two states with least flux between them as start and end states. Then we randomly sample 900 start and end frames from the corresponding states, and those frames are used as the conditions in the interpolation inference process. The generated trajectories undergo the same featurization process, and then projected on the TICA components defined by the reference trajectories. They are further discretized according to the reference metastate assignments, and a new MSM is performed on the discretized generation trajectories.
To compare the generation with reference trajectories, we compute the JSD over the metastate occupancy probabilites. To evaluate interpolation sampling quality, we compute the average path probability, valid path rate, and valid path probability as described in Jing et al. (2024c). The average path probability the average of all paths' likelihood for transitioning from the start the end. The valid path rate is the fraction of paths that successfully traverse from the start to the end. The valid path probability is the average of all valid paths' likelihood (excluding zero probbabibbbi paths). To fairly compare the generation and MD oracle, we truncate the MD oracle trajectories to varying time length, and sample 900 transition paths based on the MSM constructed from the metastates. With the sampled transition paths, we can compute the JSD over metastates, average path probability, valid path rate, and valid path probability of MD oracles.
B.4 UNCONDITIONAL. GENERATION DETAILS
Training. Training conducted by denoising randomly sampled 2.6 ns segments (500 frames) from the training trajectories. For QM9, we utilize 8 NVIDIA RTX A4000 GPUs with an effective batch size of 32 (4 samples per GPU), training the models for 400 epochs.
For each molecule in the test set, we generate ten independent 2.6 ns segments (500 frames each). Distributional histograms are then computed from these generated trajectories and compared against those derived from four reference 5 ns molecular dynamics (MD) trajectories. Results reported for this model setting for QM9 include both the standard test in Section 5.3 and enlarged test set in Section A.3.2-A.3.3
Evaluation.
B.5 FORWARD SIMULATION DETAILS
Training. Training is conducted by randomly sampling 251-frame segments at a 5.2 ps frame rate and demoising the subsequent 250 frames (corresponding to 1.3 ns), conditioned on the initial frame-O. For the Drugs and Timewarp dataset, utilize 8 NVIDIA RTX A4000 GPUs with effective batch size of 32 (2 samples per GPU with gradient accumulation steps). training the models for 400 epochs.
25

---

Published as a conference paper at ICLR 2026
Evaluation. For each molecule in the test set, we generate five forward roll-outs of 5.2 (1,000 frames total), each conditioned on the first frame of a reference trajectory. Distributional histograms then computed from the generated trajectories and compared against those obtained from four reference ns molecular dynamics (MD) trajectories. For a fair comparison, we truncate our generation trajectories to the same length as the reference trajectories in evaluation. Results reported for this model setting for Drugs are based on the standard test set in Section 5.4.
B.6 INTERPOLATION DETAILS
Training. Training is conducted by randomly sampling 101-frame segments at 5.2 ps frame rate and denoising the middle 99 frames (corresponding ==0.52 ns), conditioned on frame-0 and frame- 100. For the QM9 dataset, we utilize 2 NVIDIA A100 GPUs with an effective batch size of 128 (64 samples per GPU), training the models for 300 epochs. For the Drugs dataset, we utilize NVIDIA A100 GPUs with an effective batch size of 32 (8 samples per GPU), training the models for 400 epochs.
Evaluation. For each molecule in the test set, we perform featurization, dimensionality reduction, and clustering on the reference trajectories. We then construct an MSM on the discretized trajectories and retain only those test molecules for which all microstates from clustering are represented in the MSM. After filtering, this yields 124 QM9 and 36 Drug test molecules. Due to computational constraints, subsample 80 QM9 molecules while using all 36 Drug molecules for inference and evaluation. For each selected test molecule, we generate 900 interpolation trajectories conditioned on 900 sampled start and end states. For each MD oracle length, also sample 900 transition paths. We report the average results across all molecules successfully modeled by the MSM, as shown in Section 5.5, Figure 5, well Section A.2, Figure 6 (see details in Section B.3.3).
C METHOD DETAILS
C.I MOLECULE INPUT REPRESENTATION
Throughout our framework, input molecules are represented as 2D heterogeneous graphs. The bonding network includes both the original bond types present in the molecule and additional higher- order edges that we incorporate. Specifically, we include edges up third-order for both the QM9 and Drug datasets. Following the approach of Shi et al. (2021b), this augmentation is designed to facilitate more effective information transfer between atoms involved in bond angle and torsion angle interactions.
Table 14: Atom and bond embedding specifications.
Embedding Type
Input
Dimension
Atom Embedding
Atomic Number
30
Bond Embedding
No Bond, Bond Type, 2nd/3rd-order edge
4
We defined learned embeddings for atom type as well as bond type. Moreover, we also provide input node features per atom, largely based on Ganea et (2021). Below, we provide table with these details. These two information sources, the learned embedding and input features, as combined in our embedding module as described in Section C.2.
C.2 ARCHITECTURES
Embeddings. Across all of our models- both conformer and trajectory- we use a hidden dimension of 128 and diffusion timestep embedding dimension of 32. For molecular embeddings, we combine atom type embeddings and atom-level features via a single linear projection: Rnode.dimm wtt.ee..mmrr..ooo Brode_aim
BASICES, As introduced in Section 4.3, our BASICES architecture consists of 6 Equivariant Graph Convolution (EGCL) layers, following the formulation in Satorras et al. (2021b). To promote
26

---

Published as a conference paper at ICLR 2026
Table 15: Node feature vector based on atom-level properties.
Atom Features
Indices
Description
Options
Type
0-1
Aromaticity
truc, falsc
One-hot
2-7
Hybridization
sp. sp", sp" sp d, sp d,, other
One-hot
Partial charge
Value
9-16
Implicit valence
2,2,3,4, 6, other
One-hot
17-24
Degree
2, 6, other
One-hot
25-28
Formal charge
-1, 1, other
One-hot
29-35
ring of size
5, 6, 7,8, 8, other
k-hot
36-39
Number of rings
0, 1, 2,
One-hot
40-42
Chirality
CHI TETRAHEDRAL CW,
One-hot
CHLTTETRAHEDRAL.COM unspecified/other
interaction between invariant and equivariant representations, we insert a Geometric Vector Per- ceptron (GVP) (Jing et al., 2021) transition layer after each EGCL block. The full model contains approximately 918K parameters.
EGINTERPOLATOR. As described in Section 4.3, EGINTERPOLATOR extends BASICES by introducing temporal attention to model dependencies across trajectory frames. Specifically, we incorporate the Equivariant Temporal Attention Layer (ETLayer) from Han et al. (2024) to capture temporal structure through attention mechanisms. The architecture is constructed by stacking an additional sequence of ETLaayrr EGCL, ETLayer on top of each pretrained EGCL layer from BASICES, as illustrated in Figure 2. We retain the use of GVP-based transition layers and introduce LayerNorm (Ba et al., 2016) at key interpolation steps to improve numerical stability. The resulting model comprises 6 layers and contains 3.3M parameters in total, with 2.3M trained during trajectory finetuning the EGINTERPOLATOR framework.
C.3 CONDITIONAL GENERATION
We control conditional generation by setting appropriate entries of a conditioning mask m to either 1 or O. Let m a| denote the conditioning status for frame and atom We define mask:
Forward simulation:
[
t= otherwise
m[t,:]
0
Interpolation:
1
Ee MM (M is index of the final frame)
[1,
0 otherwise
In the unconditional setting, we default to m[:::] = 0. To incorporate this conditioning information, we use condition state embedding added to the invariant node features, with the same hidden dimension the main model. The conditioning mask is also used to restrict the denoising process and loss computation to frames where m
C.4 KABSCH ALIGNMENT
Inspired by Xu et al. (2022), we propose to use trajectory-level Kabsch alignment to find the optimal rotation and translation between the noisy trajectory x!! and the input trajectory xi step т. This corresponds to the following optimization problem:
(T) diffusion
R t = arg min Rx [7] + x
(9)
Rtt
27

---

Published as a conference paper at ICLR 2026
In practice, this can be realized by extending the original Kabsch algorithm (Kabsch, 1976) on the set of points with the temporal dimension T combined into the number of points dimension N, that forms point cloud with effective number of points T N. Afterwards, re-compute the target noise based on the aligned x! R R'xl"1 t* and the clean data x by the forward diffusion process, and then match the output of EGINTERPOLATOR towards re-computed noise é after alignment.
C.5 BASELINES
Autoregressive Models. In the autoregressive baseline setup, molecular dynamics trajectories are modeled under the Markov assumption, where the ModellEEGN (Satorras et al., 202 lb), Equivariant Transformer (Thölke & Fabritiis, 2022), GeoTDM (Han et al., 2024)- transition distribution p(I++1, ..)) To ensure fair comparison, we keep timestep intervals and frame counts consistent across all datasets during both training and inference, matching the settings used in our proposed methods. For EGNN and ET, we adopt identical configurations with six stacked EGCL or Equivariant Transformer blocks, respectively, to maintain experimental parity. For TDM the model is trained as two-frame diffusion process, with the first frame serving as conditioning, effectively reducing
the
next-step forward simulation model.
GEOTDM. The training setup and embedding configurations for our implementation of GEOTDM are aligned with those used in our proposed framework. Following the architecture described in Han et al. (2024), the model consists of 6 stacked layers of EGCL and ETLLayer blocks, resulting in total of 1. 1.4M parameters.
D PROOFS
D.1 PROOF OF THEOREM 4.
For better readability we restate Theorem 4.1 below.
Theorem 4.1. Suppose EØ perfectly models od (x) and c interpolation in Eq. 3 implicitly induces the distribution gmd (x( mdd (x(TT) ( 3mgm (x( for Egr where 3 = --a and jmd = -I[=00 p (x(()).
end perfectly models p pmd (xe then the
Proof. Upon perfect optimization, we have the connection between the denoiser and the score of the underlying distribution (Song & Ermon, 2019; Song et al., 2021):
e/ (xL) T) -I a, V (x(1), vO Tost<T-LOSTST
(10)
and similarly,
md 0,0 [x
[T) 7) = -V - o V (x STSTST.
(11)
By leveraging Eq 10 for all frames S < T 1, we have
amd
(eg (1) 1- T-1 v1 a V log gdd (x! (x
(12)
where gmd [T) is the joint of i.i.d. framewise distributions p(x). Combining with the interpolation rule in Eq. 3, we have
c6 =
1
C,,0
md
a ad
(13)
1 1-
1
(-V1- ar))
V log md (x( -T-a V log (rdddx( (x((TT)
(14)
T-ax
(-VI- ā.)
(BV log ( (x (T] (1 B3VV log gmd (x(
(15)
where B = Now, consider the distribution
x (xd (xl2T) y gud (x 1
we have
log jmd (x! BV log p md (x! (1 B3 Bmd (x!
(16)
28

---

Published as a conference paper at ICLR 2026
Therefore, Co -v1- a, V log prnd (x(")). This verifies that the interpolation rule implicitly induces the distribution gmd (x(2)) with 6g its network. Furthermore, the induction is unique, since for any distribution g(x(1) satisfying Eg -v1 ar V log ((x("1), have that v llgg 1lo ) v log (xx(")) which gives us g(x(")) p(x("1) due the property of Stein score as demonstrated in Hyvärinen & Dayan (2005); Song & Ermon (2019).
D.2 PROOF OF EQUIVARIANCE
Theorem D.2. EGINTERPOLATOR is SO(3) -Qluv-equiaaiiant and translation-invarinn Namely, R.f (x(T.)- = fEGI(Rx!"] + t), all rotations R. and translations where fEGI is the mapping defined per EGINTERPOLATOR.
Proof. Recall the definition of the interpolator:
.n [T] 60,0 T) am (1 aa) " (x!""] gnd ,7),
end [Eğ (x D
(17)
with the parameterization </ (x!"7) emd 7) SP (x- + 2md , X suffices show that the temporal interpolator cotation-equivarinn and translation-invartee of the structure model eş² directly follows the original work of Satorras et al. (2021b). For any
since the equivariance
g = (R, t) E SE(3), we have [E] (Rx!" (t) + +.,))"= R[E (xf -))-- Remd, By the proof in Han et al. (2024), we have that the temporal network 8² is SE(3)-equivariant, i.e.,
(R( + amd) + t, = Rs (x,"1 + and -) +
(18)
Therefore, we have
md 00
(Rx.") [T) + +t, = aRé md + (1 - a) (s (R(x!")
!T'l + emdd + t, Rx t). -t).
(19)
= =aRe md + (1 a Re (x! [T] and emd, -),
(20)
= Re (x, 71 r),
(21)
which concludes the proof.
29

---

Published as a conference paper at ICLR 2026
E ADDITIONAL RESULTS
E.1 CONFORMER PRETRAINING: QM9
ris
Fime keaghtre
Band koah
Sled anggle (RMEE)))
(led angle (SACA))
wight (TOda)
(bodd
Figure 10: Distributions computed from reference conformers shown in red, Checkpoint 539 in green, and Checkpoint 99 in purple. We that 539 aligns more closely with reference distributions across all collective variables and shows improved discretization of torsional states.
Above we show the additional plot associated with Section 5.1 and A.1. The plots above correspond to the following molecules (left to right):
N#C [C@] ] (0) (CO) cCO, C C[Ce0H] (0) [cеeH] (CO) CC#N, C [CC@H)] (0) ccocco, cC [CeeH] (CC=O) [сеен] (C)
E.2
SPEEDUP ANALYSIS
Table 16: Average time (s) taken to generate trajectory
Dataset & Duration
OpenMM MD
4x Block Diffusion
Full Diffusion
Drugs (5.2 ns)
584.52
201.70
161.08
QM9 (2.6 ns)
151.38
60.08
30

---

Published as a conference paper at ICLR 2026
E.3
UNCONDITIONAL GENERATION: QM9
Feature No.
Festure No.
Festure Mh
Festure
7-
7-
longth (nm)
ongth
longth (nm))
longth (nm))
1-
No.
G-
7-
angle (rad)
angle (rac)
angle (rad)
angle (rad)
Feature No.
Feature hoo
Festure
angle (rad)
angle (rad)
angle (rad)
Torsion angle (rad)
Distributions computed from reference QM9 trajectories (red), EGINTERPOLATOR (green), and GeoTDM (purple). Across all examples, framework more closely matches the reference distributions across all collective variables and better captures torsional state discretizations than GeoTDM.
Figure 11:
The figure above provides additional examples corresponding to the distributional analysis in Sec- tion 5.3. The molecule featured in the main paper in Figure 4A and 4B is:
CC [CCH] (C#CC=0) CO
The plots above correspond to the following molecules (left to right):
C# C#CC00 (C8ен] CC, cC [cee] (CHN) (CO) OC, coccco, сC[cен] (CHCC=O) co
31

---

Published as a conference paper at ICLR 2026
E.4
FORWARD SIMULATION: DRUGS
Reference
Ours
GeoTDM
Torsion 0
Autocorrelaion
Autocorreaaion
Torsion 1
Autocorrelation
0.75
0.75
0.75
Torsion 2
Torsion 3
0.50
0.50
0.50
0.25
0.25
0.25
0.00
0.00
0.00
10a
10a
10a
10
10a
10a
10a
10a
10a
Lag time (ps)
Lag time (ps)
Lag time (ps)
Reference
Ours
GeoTDM
1.00
1.00
1.00
Torsion
Torsion 1
Autocorelation
0.75
Autocorrelatio
0.75
Autocorrelation
0.75
Torsion 2
Torsion 3
0.50
0.50
0.50
Torsion 4
0.25
0.25
0.25
0.00
0.00
0.00
10a
10a
10a
10a
102
10a
10a
102
10a
Lag time (ps)
Lag time (ps)
Lag time (ps)
Reference
Ours
GeoTDM
1.00
1.00
1.00
Torsion 0
Autocorelation
Autocorelation
Autocorrlattion
Torsion 1
0.75
0.75
0.75
Torsion 2
Torsion 3
0.50
Torsion 4
Torsion 5
0.25
0.25
0.25
0.00
0.00
0.00
10a
102
10a
10a
102
103
10a
102
10a
Lag time (ps)
Lag time (ps)
Lag time (ps)
Figure 12: Autocorrelations of individual torsion angles for an example molecule, comparing reference trajectories with generations from EGINTERPOLATOR and GeoTDM. For the challenging task of capturing temporal de-correlation behavior, EGINTERPOLATOR closely follows the reference dynamics, whereas GeoTDM fails to model hame-to-frrme correlations effectively.
The figure above provides additional examples corresponding to the dynamical analysis in Section 5.4. The molecule featured in the main paper in Figure 4E-G is:
O-C (O) [nH] c2cea (C1) cc2c1CC (-O) NICCN (c2ccccc2) CC1
The plots above correspond to the following molecules (left to right):
Colcce (C) e (CN2C (-0) (CCC0C3) C2-0)
COc1 (=0) (=0) <2cce3e (c2) Cc2ccccc2-3) enl,
c0c1cca (S (=0) (=0) Nc2c (C (=0) 0) [nH] c3ccccc23) c (0C) c1
32

---

Published as a conference paper at ICLR 2026
2.00
15 1:20 10
5.1
02
eds
5:00
0.15
0.2
61
20
Distibbttin
Distribution
Distribution
Bond Angle D'stribuiion
Distroution
Tea ande
Toston (rad)
engle
Teniee
Tonton angle
Distributions computed from reference Drugs trajectories (red), EGINTERPOLATON (green), and GeoTDM (purple). Across all examples, our framework aligns closely with reference distributions across all collective variables and exhibits improved torsional state discretization pared to GeoTDM.
Figure 13:
The figure above provides additional examples related to the distributional analysis in Section 5.4.
The plots above correspond to the following molecules (left to right):
NS (=0) (=0) cll cce (CCNC (=0) coc (=0) CN2C (=0) [C@H] 3CCCC [C0H] 3C2=0) cc1, COclcce (=0) N2CCc3cc (OC) e (OC) cc3C2) ccloc,
Cclccc2c n (CCCCO) C2=0,
COC CCC.(= oc3ec (OC) ccc23) CC1,
CCOC C [CC0 (CC (=0) NCc3cce (CC) cc3) C (=0) N12
33

---

Published as a conference paper at ICLR 2026
E.5 ENERGY EXAMPLES: QM9 AND DRUGS
Table 17: Top:
Mean and standard deviation (Hartrees) of energies for selected QM9 test molecules, comparing ground-truth (GT), EGINTERPOLATOR and GEOTDM. Bottom: Block-wise energy means and standard deviations for selected Drugs test molecules, showing how EGINTERPOLATOR tracks GT distributions across successive diffusion blocks.
SMILES
GT
EGInterpolator
GeoTDM
CC(CONCOJCCиN
440.287 + 0.005
-440.249 + 0.036
438.206 +: 1.813
COC[C@ COC[C CJCCOCCC
441.428 + 0.008
-441.364 + 0.075
439.407 +: 3.932
COCCCC@HOCC
-38888299 + 0.006
-388.225 + 0.117
385.743 2.259
CCOCCCNICCI
-405.525 0.007
-405.387 0.426
-402.751 3.424
CC{=OCC@CCOO
-400.165 + 0.007
-460.140 = 0.021
-458.121 + 1.225
CCCC@
-390.780 + 0.006
-390.733 + 0.026
-387.954 + 3.434
@ H[CCC
-42..413 + 0.009
425.372 = 0.066
423.323 + 5.039
CCoLCe @HCC
-425.364 0.008
-425.326 0.045
-423.153 4.070
HOCCCIC@HIICNIC
405.507 + 0.008
-405.433 = 0.047
-403.101 + 4.087
CCC@HCC(CJ
-389.883 + 0.007
-389.547 + 0.035
-386.846 + 2.405
SMILES
EGInterpolator Block
Energy (Hartrees)
GT
-960. 102 0.010
Block 1
96000662 +: 0.020
Block
-960.027 0.167
Block 3
939. 0.307
Block 4
-960.037 0.044
GT
1185,987 +: 0.012
Block
1185.837 1: 0.241
Block 2
1185,846 1 0.168
Block 3
-188.7785 0.324
Block 4
-1185.854 + 0.133
GT
2171.285 1. 0.013
Block
2171.224 1 0.062
COOCCOIICCHIICCHCCCCOMCCOOCCCCCO
Block 2
2171.212 1 0.058
Block 3
-2171.195 # 0.060
Block 4
-2171.167 + 0.105
34

---

Published as a conference paper at ICLR 2026
E.6 INTERPOLATION: QM9
3ata
Figure 14: Generated QM9 interpolation trajectories from EGINTERPOLATOR, projected on the reference surface. The red point denotes the start frame, and the orange point denotes the end frame. The reference surface colored by metastate assignment. Each row corresponds different molecule, and each column shows generated interpolation. These examples illustrate the model's ability to generate efficient and meaningful transition paths.
The figure above provides additional examples related to the analysis in Section A.2.
The trajectories correspond the following QM9 molecules (top bottom):
C#C [cee] (0) (CC) coc, N#CC [CêH] (0) CCCO, C [CeH] (C=0) NCC-O, CCC [cеeн] (0) CCAN
35

---

Published as a conference paper at ICLR 2026
E.7 INTERPOLATION: DRUGS
Figure 15: Generated Drug interpolation trajectories from EGINTERPOLATOR, projected onto the reference surface. The red point indicates the start frame, and the orange point indicates the end frame. The reference surface is colored by metastate assignment. Each row corresponds to a different molecule, and each column shows a generated interpolation. These examples highlight the model's ability to generate efficient and meaningful transition paths.
The figure above provides additional examples related to the analysis in Section 5.5. The molecule featured in the main paper in Figure 5B is:
Q=C (CCCSc1 (CCCSc1nc2cccedc) nc2ccccc2 [nH] 1) NCc1 cccce17
The trajectories above correspond to the following Drug molecules (top bottom):
COc1 ece (S (=0) (=0) Nc2c (C (=0) 0) [nH] c3cccce23) c (CC) c1, (C) c3cccce3c21, O=C (clcce (Br) o1) NICCN (c2cccccFF).) cc1,
Cn1c (C (=0) NCCN2CC0CC2) cc2o (=0) (=0)
cCoC (-0) cle (C) (C) CSc1cc
36

---

Published as a conference paper at ICLR 2026
E.8
MIXING PARAMETERS: INTERPOLATION RESULTS & EGINTERPOLATOR -IMPLE
Valuet Aipha Parmmbbrrzz
Woussssppe layer agpho Parmmitters
Figure 16: Top: Logits of for each spatial and temporal layer after convergence on QM9. Bottom: Logits of a for each spatial and temporal layer after convergence on DRUGS. Both: Results obtained with EGINTERPOLATOR CASC for the interpolation task.
Logt ValtVa for Parmmatas JU
Logh Valuet per Layer Fammete
410
410
440
Logits of for each spatial and tempo- ral layer after convergence on the QM9 unconditional generation task.
Logits of for each spatial and temporal layer after convergence on the DRUGS forward simulation task.
Figure 17: Results obtained with EGINTERPOLATOR
-TOMSSS SIMPLE.
37

---

Published as a conference paper at ICLR 2026
F STATEMENTS AND DISCUSSIONS
F.1 LIMITATIONS CONT. AND FUTURE OPPORTUNITIES
Our results demonstrate that structural pretraining significantly enhances all-atom diffusion models for simulating molecular dynamics trajectories, especially on chemically diverse set of molecules. Nonetheless, our work has limitations that highlight directions for future research. As noted in Section 6, machine learning methods still lag behind ground-truth MD simulations in terms of physical accuracy. Future work may therefore explore improved learning objectives, molecular parameterizations, and the incorporation of physics- based regularization help bridge this gap.
While our focus was primarily on the challenging domain of organic small molecules and addresses generalizeability in this chemical space, molecular dynamics is broadly applicable other N N-body systems, such as a peptides and protein-ligand complexes. While our efforts touched these realms, future work may robustly extend framework, leveraging pretraining and structure prediction models, along with other physics-basee basee or experimental signals, to enable generative modeling of larger bio-molecular simulations. Moreover, while we have shown promising results, continued efforts should look to unify the unique dynamics of small and large systems, as well as span multiple tasks.
Additionally, although our approach effectively reproduces distributions and dynamics consistent with classical mechanics, it remains subject the inherent biases of molecular dynamics simulations. Future research may explore aligning both conformer and trajectory generation more closely with Bolzzman--ditrriuute energy landscapes improve thermodynamic fidelity.
F.2 ETHICS AND IMPACTS STATEMENT
This work develops generative models for molecular dynamics to advance efficient, accurate sim- ulation chemistry and biology. While such models can accelerate scientific discovery, they also raise concerns around AI safety and dual-use risks, particularly in the design of harmful chemical or biological agents.
Our goal is support beneficial applications in drug discovery, materials science, and molecular understanding through data-efficient and physically grounded modeling. All models are trained on publicly available, non-sensitive data and are released under open licenses promote transparency and responsible use. We encourage continued dialogue on the safe development and deployment of generative AI in the physical and natural sciences.
38


Reviews:
[{"review_id": "tZ30JBR8CA", "reviewer": "Reviewer_eveP", "summary": "The paper proposes to learn generative models of MD trajectories by fine-tuning conformer generative models. This is done by adding additional temporal layers to the conformer generation model and fine tuning on dynamics trajectories. The model is evaluated on simulations of small druglike molecules from QM9 and GEOM-DRUGS, where it roughly reproduces static and dynamic observables.", "questions": "No specific questions", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "The approach is very sensible - developing full-trajectory models by fine-tuning static structure models is an approach that many later works will likely follow.", "weaknesses": "**Novelty**\n* The authors' contribution amounts to the incorporation of conformer pretraining for MD trajectory generation, which in my opinion is not significant or non-obvious enough for a conference paper in the absence of compelling results.\n\n**Significance**\n* The task of MD trajectory generation for small molecules is of unclear utility. I am sympathetic that the authors are following prior precedent, where small molecule conformations have historically served as testbeds for modeling larger systems. However, as the AI for science field matures, it is important that the community stays focused on forward-looking applications.\n\n**Experiments**\n* The authors write \"In contrast, our method generalizes more readily across arbitrary molecular systems,\" yet do not show experiments on peptides or proteins, which would allow proper comparisons with previous work.\n* The result that the model outperforms AR baselines is not surprising, given prior work (MDGen).\n* From the results shown in Figure 4, it appears that the model has a lot of trouble matching ground truth distributions of bond lengths, torsion angles, and autocorrelation decays.\n\n**Method**\n* The linear interpolation of the temporal module output seems rather contrived, especially the thereotical justification. There are no ablation studies showing why this additional complexity is necessary.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZamzVQpdNL", "reviewer": "Reviewer_dsY1", "summary": "Continuing on previous work in the field authors propose a diffusion model for molecular dynamics (MD) trajectories of small molecules. Specifically, they propose a decomposed approach where they divide the task into modeling valid 3D structures (per frame conformers) as the first pre-training task based on larger conformer datasets, ensuring structural validity and generalizability, and then learning a temporal interpolator to realize valid MD trajectories. Introducing a structure pre-training task for a dynamics model seems well-motivated.", "questions": "Could you elaborate on the justification for the convex combination in comparison to a simpler approach that uses per-frame marginals (pre-trained with all the data, including sampled MD frames) to adjust interpolator scores? The architecture that the authors use for the interpolator, equivariant temporal attention network, already includes analogous alternating per-frame and temporal updates. The temporal interpolator could still take ${\\hat\\epsilon}^{md}$ estimates as input, ensuring that its role would remain similarly light, offering (only) temporal corrections, aligning well with the motivation start at lines 231. I understand that the authors do freeze pre-trained ES layers in their approach.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is technically well-written and derivations seem correct. Broadly speaking the proposed decomposition is also well-motivated. I particularly like introducing a marginal distribution over 3D structures (conformers) as a pre-training task so as to ensure structural validity across trajectories and transfer across molecules. The approach is also in principle extendable to larger molecules such as (small) proteins. \n\nThe proposed temporal interpolator seems to capture some measures of temporal dynamics (autocorrelation) better than alternatives such as GeoTDM as shown in Figure 4 E/F.", "weaknesses": "The per-frame marginal distribution over conformers could be perhaps more cleanly separated as a learning task. As a pre-training task, the model could be estimated from larger conformer datasets and then separately fine-tuned based on subsampled frames from MD trajectories prior to learning any temporal dynamics. It seems unnecessary to further adjust this part. Indeed, a product distribution over the frames would serve as a proper tilting function for learning a light temporal interpolator (tilted analogously to reward guided sampling). It is unclear to me why authors adopted a more convoluted convex combination that is learned from trajectories (with some frozen layers).\n\nWhile theorem 4.1 appears correct, it also highlights potential issues with the approach. The resulting intermediate target distribution seems undesirable with the 1/(1-alpha) exponent.\n\nThe primary comparison results in Table 1 pertain to per-frame metrics except TICA. For this reason, authors' own pre-trained per-frame model (or any other per-frame model) would do well for most of these metrics, requiring no temporal interpolator. It would be helpful to focus primarily on evaluation of dynamics since this extension is the key contribution in the paper, not conformer generation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4XmjMmr8b2", "reviewer": "Reviewer_YkBB", "summary": "The paper proposes a two-stage framework for generating molecular dynamics (MD) trajectories using diffusion models. First, they train a large structure diffusion model on static molecular conformers (like QM9, GEOM-Drugs). This model learns how valid 3D molecular structures look like. Subsequently, they freeze it and train a smaller temporal interpolator on a limited set of MD trajectories. This temporal module learns to align the static structures in time, adding smooth and physically consistent motion between them. The combined system, called EGINTERPOLATOR, can generate realistic molecular trajectories even when there’s very little MD data available. It also keeps SE(3)-equivariance and can handle different generation modes (simulation, interpolation, etc.).", "questions": "1) How stable are the generated trajectories over long time horizons? Do they drift away from realistic energy basins?\n2) Could the temporal interpolator be trained or conditioned on energy or force information to improve physical consistency?\n3) Could the method handle non-equilibrium or biased simulations?\n4) What’s the computational cost compared to training a full end-to-end trajectory diffusion model?\n5) Have you run experiments that in the limit sample from all meta-states from a single starting red point in appendix E6 and E7?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- The idea to separate spatial structure learning from temporal dynamics is elegant and practical. It reduces data requirements and improves generalization.\n- The temporal interpolator design is well conceived — it works as a learned guidance or adapter that connects independent conformer frames into a coherent trajectory.\n- Experiments are convincing, with good results on QM9 and GEOM-Drugs datasets. The model seems to generate smoother and more realistic bond and torsion distributions than baselines.\n- It’s well grounded in symmetry (SE(3) equivariance), which is crucial for molecular data.\n- Conceptually it’s similar to the trend in video diffusion models, but nicely adapted to the molecular domain.", "weaknesses": "- The physical validation is lacking — results are mostly on geometric statistics. No tests about energy conservation, temperature stability, or realistic MD physics.\n- The method depends a lot on the pretrained conformer model. If that model is not good, the whole system might fail.\n- It’s not clear how this would scale to bigger molecules (like proteins) or longer trajectories.\n- The temporal module is still a bit of a black box. The paper doesn’t show much intuition about what it actually learns.\n- Fine-tuning with small MD datasets could overfit, and the paper doesn’t really study that.\n- Fundamentally, the architecture setup is still sequential when generating whereas BioEmu for example targets the equilibrium distribution directly.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BdDL4jvaMn", "reviewer": "Reviewer_c4YK", "summary": "This paper presents EGInterpolator, a framework for generating molecular dynamics (MD) trajectories by leveraging structure pretraining. The key idea is to first pretrain a diffusion model on large-scale conformer datasets, then introduce a temporal interpolator module trained on limited MD data to enforce temporal consistency.", "questions": "1. How much conformer data is actually needed? What if you pretrain on a smaller, more targeted set of conformers? This would help understand the data efficiency of your approach.\n2. You train separate models for QM9 and Drugs. Have you tried training a single model on both datasets? What prevents the method from generalizing across different molecular systems in a unified way?\n3. What about long-time stability - do generated trajectories eventually diverge or produce unphysical configurations?\n4. Table 5 shows some degradation in later blocks for forward simulation. How many blocks can you roll out before quality becomes unacceptable? Is there a way to prevent this deterioration?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The authors test their method across multiple tasks (unconditional generation, forward simulation, interpolation) and provide extensive metrics including JSD for various metrics. The ablation studies are quite thorough.\n2. Using structure pretraining to leverage abundant conformer data is a sensible solution that makes practical sense.\n3. The method outperforms baselines and performs impressive results on the interpolation.", "weaknesses": "1. The experiments are restricted to small organic molecules (QM9 has molecules with ≤9 heavy atoms). While the authors acknowledge this in limitations, it's unclear how well this approach would scale to larger, more practical systems like proteins or protein-ligand complexes. The method's utility for real-world drug discovery applications remains uncertain without demonstration on larger molecules (As far as I knew, there are also large molecules in GEOM dataset).\n2.  In several metrics, the model performs worse than even short MD oracle trajectories. This suggests the generated dynamics may be too fast or not physically accurate enough for practical applications. The authors should discuss this gap more critically.\n3.  Theorem 4.1 shows the interpolator induces an intermediate distribution, but why this particular interpolation strategy is optimal, and how the choice of α affects the bias-variance tradeoff.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "x4IvrqUlWt", "reviewer": "Reviewer_yR8j", "summary": "This work introduces EGInterpolator, a novel diffusion-based model designed for modeling MD distributions. To address the data sparsity of MD trajectories, the model adopts a two-stage training strategy: it is first pretrained on a large conformer dataset and subsequently fine-tuned on MD data. A key component of the framework is a temporal interpolator, which captures temporal dependencies by integrating the pretrained unconditional generative model with a temporal network through linear interpolation. Experiments on GEOM-QM9 and GEOM-Drugs demonstrate that EGInterpolator achieves strong consistency with MD reference trajectories across unconditional generation, forward simulation, and interpolation tasks.", "questions": "1. For small-molecule systems, MD simulations using empirical force fields already offer a good balance between efficiency and accuracy. The authors should further clarify the advantages of their model over traditional MD methods or include additional experiments on more complex biomolecular systems.\n2. Line 171 defines the so-called conformer distribution $p^{cf}(x)$, which is a potentially misleading definition. It can only be well-defined if it is based on an empirical data distribution (e.g., a dataset) or a known distribution (e.g., the Boltzmann distribution). The authors should clearly specify the definition.\n3. In the MD finetuning stage, are the model parameters $\\theta$ pretrained on the conformer dataset fixed or further optimized? This point does not appear to be clearly specified in Equation (3). If the parameters $\\theta$ continue to be updated during finetuning, then the premise of Theorem 4.1 may not hold, since it would be unclear whether $\\epsilon_{\\theta}^{cf}$ remains consistent with the pretrained approximation of $p^{cf}$ during finetuning. This would undermine the practical validity of the theorem.\n4. Lines 234–235 assume an extreme case, $\\hat{p}^{md} = p^{md}$, to illustrate the advantage of the parametrization. I find this assumption inappropriate, as $\\hat{p}^{md}$ assumes all conformations are i.i.d., while there exist temporal dependencies between consecutive MD samples, making it nearly impossible for their joint distribution to coincide with that of an i.i.d. case. Could the authors provide a reasonable justification for this assumption?\n5. From the experimental results in Figure 3(A), the recall of the coverage and matching metrics on the QM9 dataset still falls short of SOTA performance. Could the authors provide possible explanations for this gap?\n6. I have concerns about the setup of the interpolation task. Even though the model can generate a trajectory from the initial to the target state through the conditioning mask, the actual transition time corresponding to this process may be longer than 0.52 ns, which could result in the generated trajectory failing to capture the true underlying dynamics. Could the authors provide an explanation for this?\n7. A typo: line 458 states that the generated MD trajectory spans 0.52 ns, whereas Figure 5D labels it as 1 ns.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The paper presents a clear research motivation and a well-organized logical flow. Considering the scarcity of MD data, the strategy of pretraining on large-scale conformer data followed by fine-tuning on MD data effectively reduces the complexity of spatio-temporal modeling of MD distributions.\n- The temporal interpolator is designed in a concise and effective manner, enabling efficient temporal modeling while preserving the structural generation capability acquired during pretraining.\n- The experiments on organic molecules thoroughly investigate tasks including unconditional generation, forward simulation, and transition path sampling, providing a comprehensive demonstration of the model’s capability to capture MD distributions.", "weaknesses": "- This work is evaluated only on small-molecule systems. However, for such systems with relatively few atoms, MD simulations using empirical force fields can achieve high accuracy at an acceptable computational cost, which may limit the practical advantages of the proposed model. The authors are encouraged to further justify the benefits of their approach over traditional MD methods or provide additional experiments on more complex biomolecular systems.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)