GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters
Authors: Wanjia Zhao
Jiaqi Han
Siyi Gu
Mingjian Jiang
James Zou
Stefano Ermon
Venue: NeurIPS 2025 poster ()
Keywords: Diffusion Models
Equivatriance
Geometic
Primary area: deep_learning
TL;DR: We propose a general approach that unlocks the transferability of geometric diffusion models.

Abstract: Geometric diffusion models have shown remarkable success in molecular dynamics and structure generation. However, efficiently fine-tuning them for downstream tasks with varying geometric controls remains underexplored. In this work, we propose an SE(3)-equivariant adapter framework (GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks without modifying the original model architecture.  GeoAda introduces a structured adapter design: control signals are first encoded through coupling operators, then processed by a trainable copy of selected base model layers, and finally projected back via decoupling operators followed by an equivariant zero-initialized convolution. By fine-tuning only these lightweight adapter modules, GeoAda preserves the model’s geometric consistency while mitigating overfitting and catastrophic forgetting. We theoretically prove that the proposed adapters maintain SE(3)-equivariance, ensuring that the geometric inductive biases of the pretrained diffusion model remain intact during adaptation. We demonstrate the wide applicability of \method across diverse geometric control types, including frame control, global control, subgraph control, and a broad range of application domains such as particle dynamics, molecular dynamics, human motion prediction, and molecule generation. Empirical results show that  GeoAda achieves state-of-the-art fine-tuning performance while preserving original task accuracy, whereas other baselines experience significant performance degradation due to overfitting and catastrophic forgetting.

GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapters
Wanjia Zhao; Jiaqi Han; Siyi Gu, Mingjian Jiang, James Zou, Stefano Ermon Department of Computer Science Stanford University
Abstract
Geometric diffusion models have shown remarkable success in molecular dynamics and structure generation. However, efficiently fine-tuning them for downstream tasks with varying geometric controls remains underexplored. In this work, pro- pose an -qqui-rqui adapter framework (GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks without modifying the original model architecture. GeoAda introduces structured adapter design: control signals are first encoded through coupling operators, then processed by a trainable copy of selected pretrained model layers, and finally projected back via decoupling operators followed by an equivariant vero-initialized convolution. By fine-tuning only these lightweight adapter modules, GeoAda preserves the model's s geometric consistency while mitigating overfitting and catastrophic forgetting. We theoretically prove that the proposed adapters maintain SE(3))cquivariann ing that the geometric inductive biases of the pretrained diffusion model remain intact during adaptation. We demonstrate the wide applicability of GeoAda across diverse geometric control types, including frame control, global control, subgraph control, and broad range of application domains such as particle dynamics, molec- ular dynamics, human motion prediction, and molecule generation. Empirical results show that GeoAda achieves state-of-the-art fine-tuning performance while preserving original task accuracy, whereas other baselines experience significant performance degradation due to overfitting and catastrophic forgetting.
ensur-
Introduction
Diffusion models have emerged as powerful generative frameworks across wide range of domains,
including image synthesis [44, 38], robotics [36, 27]. and molecular generation [23, 41, 39, 42). In particular, geometric diffusion models [11] which incorporate spatial and symmetry- inductive biases have shown strong empirical performance in tasks such as particle dynamic prediction [15, 17, 28), molecular generation [3, 14] and protein-ligand binding structure prediction [8]. By modeling data in an equivariant network, these models are able to capture complex geometric relationships essential for physical and chemical systems.
However, despite their strong task-specific performance, existing geometric diffusion models lack the ability to generalize across tasks. In particular, it remains unclear how model pretrained on one geometric generation task can be effectively adapted new task involving additional or different control signals. This limitation is especially pronounced in real-world molecular applications, where the available data across tasks are often highly imbalanced, and collecting labeled pretraining data for every new condition is costly and time-consuming. Without a mechanism for transfer, models must be retrained from scratch for each new task, which is inefficient and often leads to overfitting or loss of previously learned capabilities.
Equal contribution. Correspondence to wanjiazh iiliiaaa@cssssaaoor.... wt..ooooord.cdu Code available here.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Geometric Control
Preirained Task
Pretratned Denotber
Equirariunt Adaatters
Downstream Task
Clebel
Suhgraph Cantred
Figure 1: Overall framework of GeoAda. The model integrates diverse control signals. including frame, global type, and subgraph controls through lightweight equivariant adapters inserted into the frozen pretrained denoiser.
To this end, we propose a general and efficient (GamoAark(Gee/Ada) that enables the transfer of geometric diffusion models across diverse downstream tasks with minimal computational overhead. Inspired by the success of ControlNet [44] in conditional image generation, we introduce an equivari- ant adapter module that augments pretrained geometric diffusion model with task-specific control capability. The Equivariant Adapter comprises two key components: 1) The equivariant adapter block that operates through structured requence-wher control signals are encoded via coupling operators, processed by a trainable copy of selected pretrained model layers, and then decoded via decoupling operators. 2) Equivariant zero convolution, which acts safeguard for the original score by zeroing out the conditional contribution at initialization without blocking gradient updates. This design preserves the model's -quivaannu and allows modular, task-specific adaptation without altering the original model architecture. In addition to being lightweight and flexible, the adapter is parameter-efficieet and implicitly regularized, thereby mitigating overfitting and preserving the performance of the pretrained model.
In summary, we make the following contributions: 1. We propose an equivariant adapter framework (GeoAda) for geometric diffusson models that enables efficient task adaptation with minimal overhead. The adapter modules are lightweight and operate as Alug-and-play components, allowing flexible conditioning on new control signals without architectural modifications to the pretrained model. 2. GeoAda is parametee-efficieet, introducing minimal overhead for downstream tasks compared to full fine-tuning, which updates the entire model and incurs substantial memory and computational costs. 3. By freezing the pretrained model and introducing trainable adapters, GeoAda imposes implicit regularization, helping to mitigates overfitting and avoids catastrophic forgetting, thereby preserving performance on the pretraining task. 4. We carefully design the adapter architecture to be SE(3)-equivariant, ensuring that the adapted model retains the geometric inductive bias and the theoretical benefits of equivariant diffusion models, including SEE3)-invariant marginal distributions during generation. 5.We evaluate GeoAda across diverse geometric control types, including Frame Fontrol, Global Type Control, Subgraph Control, and a wide range of application domains, such as particle dynamics, molecular dynamics, human motion prediction, and molecule generation. GeoAda consistently matches outperforms full fine-tuning baselines on downstream task, while avoiding performance degradation on the original pretrain task a common failure mode of naive tuning and prompt-base approaches.
2 Related Work
Geometric difflusion models. Recent diffusion models have been extended 3D geometric data, with SE(3) equivariance enabling physically consistent generation for tasks like molecular design and trajectory modeling. One of the earliest efforts, EDM [14] introduced an SEC3)eequivarian framework for 3D molecule generation that significantly improved sample quality. GeoDiff [42] pioneered this by learning stable molecular conformations through SE(3)-invariant diffusion, while GeoLDM [41, 39] advanced scalability and controllability via structured latent spaces. GCDM [23] advanced large molecule generation by incorporating geometry-complete local frames and chirality-sensitive features into SE(3) SE(3)-equivariant networks. TargetDiff [9] further extended these models to structure-base

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drug design by generating molecules conditioned on protein targets through an SE(3) -quivvaaan
processor. Beyond molecular applications. diffusion augmented with geometric inductive bias has been explored in other domains such as 3D shape and scene generation [2] and robotics [36, 27]. Beyond static geometric modeling. GeoTDM [11] and EquiJump [5] address dynamic 3D systems by introducing temporal attention mechanisms. However, existing geometric diffusion models lack cross-task generalization. Our framework enables efficient adaptation to new controls.
Finetuning for (geometric) graphs. Finetuning for geometric GNNs generally falls into two categories: prompt-bat based and adapter- based methods. Pioneering prompt-base approaches [34, 20] introduce virtual class- prototype nodes with learnable links for edge prediction pre- pre-trained models, but lack generalizability to alternative pre- pre-training strategies. Meanwhile, works like GPF [6] explore universal prompt- based tuning by adding shared learnable vectors to all node features in the graph. Adapter-based based methods, exemplified by AdapterGNN [18), insert lightweight modules into GNN layers, achieving parameter-efficient adaptation across diverse graph domains.
Finetuning diffusion models. Recent research has proposed various strategies for fine-tuning diffu- sion models with improved efficiency, control [44], and alignment [37]. ELEGANT [35] formulates fine-tuning as an reguliy-re control problem, directly optimizing entropy-enhanced rewards with neural SDEs. ControlNet [44] improves controllability by adding lightweight trainable branches to frozen diffusion backbones. Prompt Diffusion [38] enables training-free -free in-context learning for image-ta ponge-to-imane to-image tasks via example- based conditioning. However, fine-tuning diffusion models in geometric domains (e.g. particles, molecules) remains underexplored. GeoAda addresses this gap by enabling efficient and effective adaptation of diffusion models to geometric tasks.
3 Preliminaries
Geometric graphs and trajectories. We represent a geometric graph as G (V,E) where V is the set of nodes and is the set of edges. In particular, each node is equipped with certain node feature h, IR'' representing its type or physical property, and the Euclidean coordinate x, R representing its spatial position. An edge exists between node and j they bear certain connectivity through, e.g., chemical bonds, or spatial proximity with distance smaller than a cutoff. A trajectory a generalization of geometric graph the dynamical setting where the coordinates x!"" E 3R3xT are augmented with an additional temporal dimension, where 7 is the number of frames.
Geometric diffusion models. Geometric diffusion models are a family of generative models for capturing the distribution of geometric graphs and/or trajectories. Given an input data point Go. they feature a forward noising process that gradually perturbs the clean data with a transition (G-199) where Gy converges to tractable prior. A neural network co(Gr. T) (a.k.a. the denoiser) is learned to approximate the Stein score [33] through denoising score matching [31, 32, 13], which will be leveraged to derive the transition kernel Pa ( (9,) in the reverse process at sampling time. Notably, a core distinction of geometric diffusion models from others is that they enforce an SE(3)-invariant marginal, i.e.,
pe (G = pe(g Go).
Vg E SE(3),
by parameterizing the denoiser Eg with an SE(3)--quivariint architecture [14, 42], i.e.,
6olg Gr, = g tn <a(Gr, T),
(2)
where SE(3) is the Special Euclidean group consisting of all rotations and translations in 3D.
4
Method
In this section, we detail our approach, equivariant adapter for geometric diffusion models. We first specify three types of controls in $ 4.1 that are ubiquitously enforced to geometric diffusion models various downstream tasks. In $ 4.2, we propose an architecture-agnosiic and principled recipe for encoding such controls that seamlessly enables finetuning on the pretrained denoiser. In $ 4.3, we present our design of GeoAda, a plug-in-and-play adapter module tuned for each downstream task that unlocks transfcrability.
3

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4.1 Geometric Controls for Geometric Diffusion Models
In this work, we aim transfer the generation capability of pretrained geometric diffusson models to downstream tasks where additional geometric controls present. Specifically, we are concerned with three different types of geometric controls, namely global type control Cg. subgraph control Cs, and frame control Cr, as detailed below.
Global type control. Each global type control é E Cg is vector in RK describing certain global signal enforced on the geometric graph, such as an encoding of the class label, some quantum chemical property of the molecule [14], or even the embedding of some text prompt [22].
Subgraph control. Each subgraph control 9 (V, E Cs is represented as geometric graph with the set of nodes V and edges &. Subgraph control widely exists in scenarios where generating a geometric graph conditioned on another fixed subgraph is of interest. For example, in the task of pocket condet--onditioned ligand generation [8]. the protein pocket is viewed as the fixed subgraph while a geometric diffusion model is learned to generate the ligand, conditioned on G.
Frame control. Each frame control in Cj takes the form of a sequence of additional T frames, namely (1)) R for each node i. Frame controls enforced in cases when, e.g., trajectory has been partially observed and the model expected to generate the future or missing frames conditioned on the observed frames.
4.2 Encoding Geometric Controls
In this subsection, we propose simple yet effective approach for incorporating the geometric controls into the denoiser without modifying its architecture. Such feature is critical since it enables us to initialize the denoiser fully with the pretrained checkpoint when performing finetuning on downstream tasks, thus significantly alleviating optimization overheads and potential inconsistencies in the parameter space. More importantly, our design is also guaranteed to preserve the equivariance of the denoiser, a fundamental principle that leads to the success of geometric diffusion models.
In form, given the denoiser en (G,,T) we seek to devise (g T, C,C) where C Ca Cs Up is any 4.1. Our core observation lies in that each type of the control can be
of the control we specified encoded through certain coupling operator C(), of the input noised graph Gr and control C, and corresponding decoupling operator g that extracts the scores on the nodes and frames in G2 from the output of Eg. We introduce our design of f and g with respect different controls as follows.
Global type control. For global type control CG = č E gK we design as a node-wise addition of the input node feature and linear transformation of the control č, i.e., E f(V,E,C, where
V ((x:), (b, + (ε))),
E' E'=,,
(3)
where RR + " is an MLP that lifts the control signal the node feature space. We use identity function as the decoupling operator g.
Subgraph control. For subgraph control Cs = -. the coupling operator f is realized by computing the supergraph of the input & and the control $. i.e., V", f(V,E, E,C,, where
E' --E
The decoupling operator g is implemented by extracting the features of subgraph that corresponds to the nodes in the input graph G from the output of Eg.
Frame control. For frame control GF == {x( }. we implement f as concatenation of the input frames and the frame control, i.e., V", f(V, EVE,CC) C). where
V [concat(xx])) [xx (b.)).
E'=E,
(5)
and g performs the reverse operation by discarding the frames corresponding [T] from the output of Eg.
Proposition 4.1 (Equivariance of control encoding). If the denoiser Eg is SE(3)-equivarian, the composition g Eg ff also -equivraun, for all controls C E C.
4.3 Equivariant Adapters

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With the control encoding in $ 4.2, straightforward ap- proach leverage a pretrained diffusion model on down- stream tasks is to perform supervised finetuning (SFT). However, SFT usually induces suboptimal empirical per- formance, since 1. SFT is parameter- inffficer-eeffccient since each gradient update is conducted on all parameters the pre- trained model; 2. the full-pate hull-parameter finetuning is prone to overfitting with limited amount of finetuning data; and 3. the model finetuned after SFT loses performance guarantee on the original task, a phenomenon widely acknowledged catastrophic forgetting.
Goomani Cretall
lxpua Neave Greph IV,.
Cocclayg Opeaaar
F (P
Premited Dowibe back (hrred)
Tradki Deoeglin Opmane
Equivartant Adaltt
Ourpor -.70.
Figure 2: control signal is injected into the noised graph G, and processed by an equivariant adapter block. The adapter output added to the frozen denoiser and repeated B times to produce the final output.
Overall framework of GeoAda. A
To address these challenges, we draw inspiration from the successful application of adapters on image diffusion mod- els, e.g., ControlNet [45], to devise diffusion adapter for geometric diffusion models. Our approach, dubbed equiv- ariant adapter, is a lightweight tunable module plugged-in on top of the pretrained model, which is optimized for each downstream task.
The equivariant adapter block. In detail, each equivariant adapter block is responsible for processing the control signal and fusing it into the score produced by the pretrained model, whose parameters are always freezed at finetuning stage. Each adapter block consists of, in a sequential manner, the coupling operator f, trainable copy of the corresponding layers in pretrained model cØr, the decoupling operator g, followed by an equivariant zero-convolution layer.
Specifically, the composition g o Egr o f, as depicted in $ 4.2, functions altogether as a conditional score network eæ (Gr, T,C) C') that captures the bias of the control signal on the original score (G 7) while ensuring the SE(3) -equivaavve of the conditional score. Moreover, ég can be initialized as subset of the layers in the pretrained model eg. thus reducing the total number of tunable parameters compared with SFT. While the selection strategy can be arbitrary, empirically we have found that selecting the first layer for every K consecutive layers from the pretrained model performs more favorably compared with naive choices such as the initial or last several layers, under the same parameter budget (c.f., $ 5.4).
While the equivariant adapter block offers an parameter-efficien way of modeling the conditional score, its non-zero initialization introduces additional noise when it is added to the original score ég. leading to instability at the beginning of the finetuning stage. To alleviate such issue, we borrow insight from the zero-convolation module proposed in [44] that acts as safeguard of the original score by zeroing out the conditional score at initialization without blocking the gradient update.
Equivariant zero-convolution.
For any (1x,), (h.)), equivariant aero-convolution is given by
=0((x; (h:)) = (fxx (x; - x)), (phn @ h:)),
(6)
where X == Dm X; is the center-of-mass of the input graph, and Φx E Ln E R are learnable parameters initialized all as zero. By such design, we guarantee that each equivariant adapter block, when equipped with equivariant convoluonv,,,ion, yields rotation-equivarii iossslatio-invariinn output, hence the SEuii-eqqie of the conditional score after adding the output to the original score. Furthermore, the output of equivariant adapter block will always be zero at initialization, which does not affect the original score, thus enabling smooth and noiseless optimization when tuning the adapter.
and
4.4 Overall Framework
The overall framework of our adapter is depicted in Fig. 2. In general, our adapter is comprised of B equivariant adapter blocks, where each block is a sequential stack of the coupling operator f, the trainable copy of one layer of the denoiser, the decoupling operator g, and zero-convolution module. At finetuning stage, all parameters in the original denoiser are freezed while the trainable copies and coefficients in zero-convolution are updated through gradient coming from minimizing the denoising loss
Lénetume (0'netame@0.00 -o0=---vvrr.iccc-e.eeerrorrlll
+s. (0r r,C) - -c1/.
(7)
5

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where DD is the downstream dataset, 9. is the noised graph drawn from ((g- and o refers to our proposed equivariant diffusion adapter. At inference time, we use Eg Sp sy. (9 T, C) as the conditional score when computing the reverse transition kernel p(G+-119,,C).
Our GeoAda offers several key advantages over standard supervised fine-tuning (SFT):1. The adapter modules are lightweight and operate as plug-and-play components, allowing flexible conditioning on new control signals without architectural modifications to the pretrained model. 2. Parameter-efficient,, as only a subset of trainable adapter modules are introduced. 3. By freezing the Pretrained model and only optimizing lightweight adapters, the method imposes implicit regularization, helping to prevent overfitting. 4. Through the careful design of eqqivariia adapter blocks and zero convolutions, GeoAda guarantees equivariance throughout the tuning process, thereby retaining the theoretical benefits of geometric diffusion models.
Experiment
We evaluate GeoAda across three categories of additional fine-tuning controls: (1) Frame control during dynamic prediction ($ 5.1), (2) Global type control in human motion prediction($ 5.2), and (3) Subgraph control in molecule generation ($ 5.3). We also performed ablation studies on core design choices and present some observations in $5.4.
Baselines. We compare with three types of baselines: (1) Fine-tuning methods, including Full FT
which fine-tunes the entire model, and PARTIAL-K: [12, 16, 45], which updates only the last k layers of the pre-trained model; (2) Prompt-based methods, including GPF, GPF-plus [6], which both inject learnable prompt features into the input space. And Prompt-Template maps new inputs to pre-training-style inputs using manually designed graph templates, specifically for the conditional case. (3) Head-only tuning methods, where MLP-k freezes the pre-trained model and uses k-layer MLP as the prediction head. To preserve equivariance, we replace the MLP with an EGTN block in our implementation. More details can be found in App. 9.2.
The input data are processed as geometric graphs. For both trajectory and global control settings, we follow the same experimental setup as GeoTDM [11], adopting EGTN as the backbone model with three GeoAda blocks and a hidden dimension of 128. For subgraph control, the base model follows the configuration of TargetDiff [8]. We use 'T 1000 and linear noise schedule [13]. More details in App. 9.1.
Implementation.
5.1 Frame Control
Task setup. For pre-training, we use the first 10 frames as the condition and train the model to predict the trajectory over the following 20 frames. In the downstream task, we adopt different setup where the model observes 15 conditional frames and predicts the next 20 frames. We evaluate all models on both the original task and the new task to assess their generalization and adaptability across different settings.
Metrics. For conditional trajectory generation, employ Average Discrepancy Error (ADE) and Final Discrepancy Error (FDE), which are widely adopted for trajectory forecasting [43, 40], given by ADE 1'1) , ET- Dnn ||x (e) - 1l2. and FDE(x!"), ( )
a N W-1 ||x]
(T-1)
112 For probabilistic models, we report average ADE and FDE derived from K = 5 sam- ples. For unconditional trajectory generation, we report three complementary scores: The Marginal score measures statistical alignment by computing the mean absolute error (MAE) between binned distributions of model-gan generrtee and ground sification score is the cross cross-entropy of binary classifier trained to distinguish generated trajectories from real ones, offering insight into sample realism. The Prediction score measures the mean squared emror (MSE) of sequence model trained on generated data and tested on real trajectories, reflecting the utility of generated samples for downstream prediction. For more detailed metric definitions, please refer to Appendix 9.5.
coordinates (or bond lengths for MD17). The Clas-

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5.1.1 Particle Dynamic
Experimental Setup. We adopt the CHARGED PARTICLES dataset [17, 28] for particle dynamics simulation. In this dataset, N = 5 particles with randomly assigned charges of either +1 or -1 interact via Coulomb forces, resulting complex, non-linear trajectories. We use 3000 trajectories for training, 2000 for validation, and 2000 for testing. We explore two settings: (1) Conditional trajectory generation: we use the first 10 frames of each trajectory as input to predict the subsequent 20 frames during pretraining, and 15 frames as input during finetuning to predict the next 20 frames. (2) Unconditional trajectory generation: we generate trajectories of length 20 from scratch during pretraining. During finetuning, we condition on the first 10 frames and predict the next 20 frames.
Table 1: Comparisons on CHARGED PARTICLES dataset.(all results reported by x10 (t)) (L) denotes whether larger/ smaller number is preferred. "NaN" denotes generation collapse due numerical instability, typically observed in baseline models after fine-tuning on original task. "-"indicates that haseline Prompt- Tem requires explicit conditioning and cannot be applied when no conditioning frame is given.
Setting
Uncondition
Condition
Task
Downstrcam
Pictrain
Downstream
Pretrain
Metric
ADE(
FDE(J)
Marg(J)
Cluss())
Pred(L)
ADE(J)
FDE(L)
ADE(()
FDE(J)
Pretrain
nan
nan
e.009
5,149
0.109co.c04
11.826-0.135
20,395eo.2
+.172
+.815+00007
Full FT
1,93
10.014
16.761
1.025 13.000
nan
nam
L106600007
2.590
5.998
10.00
11.75
107
Prompt- Tem
1.723-n0014
10.051
nan
0am
PARTIAL-K [12]
1,685 +0.000
3,594
+0.00:
1.016
+0.000
Dan
1,409 =0,009
3,330=0.042
9.325
+0.054
11.94 +0.140
MLP-k
6.258
9.11112.4m
1.015
0.00
5.740
1 1.503
3.338:0.039
3924
3950
GPF [6]
1.643 +0.014
3,671
+0.020
1.027=eo.00
Ban
Dan
1.575 =0.017
3.390=0.030
nan
GPP -PP- [6]
1.596 10.011
3.57410.024
1,023 1000000
nan
nam
1.648
3.670_0..30
mun
nan
GeoAda
+0.019
#0.022
0.079
5.134
0.111 +0.00s
1.10==0012
+0.003
L.175+0.05
2.806
Results. We present the results in Table with the following observations. Under both the unconditional and conditional trajectory generation settings, GeoAda achieves comparable or better performance than Full FT on the downstream task (conditioning on the first 10 frames to predict the next 20), while only tuning half the number of parameters. Furthermore, it consistently outperforms other fine-tuning and prompt-based baselines, achieving 35.69% improvement on ADE and 21. 29.99% % on FDE. On the original pretraining task, all baselines exhibit substantial performance degradation, with some failing to generate valid diffusion samples, indicating that these methods suffer from overfitting and catastrophic forgetting due to excessive adaptation to the downstream task. "In contrast, by leveraging equivariant zero convolutions, GeoAda retains the pretrained model's 's performance.
5.1.2 Molecular Dynamies
Experimental setup. We employ the MD17 [3] dataset, which contains the DFT-simulated molecular dynamics trajectories of small molecules, with the number of atoms for each molecule ranging from 9 (Ethanol and Malonaldehyde) to 21 (Aspirin). For each molecule, 5000 trajectories are used for training and 1000/1000 for validation and testing, uniformly sampled along the time dimension. Different from [40], we explicitly involve the hydrogen atoms which contribute most the vibrations of the trajectory, leading to a more challenging task. The node feature the one-hot encodings of atomic number [29] and edges are connected between atoms within three hops measured in atomic bonds [30].
Noai
Figure 3: Visualization results of GeoAda on Malonaldehyde and Naphthalene from MD17 dataset.
As shown in Table 2, GeoAda achieves state-of tire--ofthee-aaa art performance across all five molecu- lar systems in the MD17 dataset, indicating strong transferability geometric diffusion models. In downstream fine-tuning task, the method consistently matches or exceeds the performance of full fine-tuning and outperforms other prior methods by an average of 18.94% in ADE and 18.22% in FDE. Importantly, when returning to the original pretraining task, it retains performance comparable to the pretrained model, while both fine-tuning and prompt-based methods exhibit significant degradation or collapse due to overfitting. More experiment results on Malonaldehyde and Naphthalene in App. 10.1.
Results.
7

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Table 2: Comparisons for Molecular Dynamics prediction on MD17 dataset (all results reported by x x1001 The best results are highlighted in bold. Results averaged over 5 runs. "NaN" denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on the original task.
Neamaritn
Aopinn
Bencond
Biuas
Metrie
ADC
FDFt
ABB
IT6
ADE
FTC
ADB
FIR
ADE
ABB
FIR
Pectuln
3:702 aume
0.24
0.30Bcc
3.260aaet
4.37
L856
355
2250
0
PARTIAL 112
1,77
1885
1 435
3,07
0.34pxxm
0 0.407ammm
0.31
0.49
1.388
2.16 muse
6 c40
4.636u
MLP-
18923a
1 157M
30
1.101a
2 poor
2.1baa
GIV (0]
5.500
4,372 caneet
IL34bes
1.230
2.42loe11
GRF plas E5
1963 10044:..0
m
2 2.33
01.34an.11
0.31 Laaon
1
1.065x.
1 es
2 muoe
3.40 muftf
4.074 axmuial
Goobde
acues
1,00
a0.00
0319.
0.340...0
0.504
5.2 Global Type Control
Experimental setup. The CMU Mocap dataset is a commonly used dataset for human pose prediction, which includes 8 action categories. A single pose has 38 body joints in the original dataset, among which we choose 25 joints following the configuration of MSR-GG GCN [4], using 10 frames as input to predict the subsequent 25 frames. For pre- tre-trraning, we construct a dataset by combining the three most frequent actions: directing traffic, washing windows, and giving basketball signals. The remaining five actions are used the downstram task fine-tuning dataset.
Results We report short-term and long-term mo- tion prediction results on the CMU Mocap dataset in Tables 3 and 4. More results on jumping and soc- cer scenarios are in App. 10.2. GeoAda consistently achieves state-of sat--offthhe-aee are performance across all ac- tion categories and time horizons. In this setting, the pretraining dataset is significantly larger than the downstream task dataset (30k vs. 245-1345 data- points). As result, naïve fine-tuning and prompt- based methods are highly prone to overfitting to the limited downstream training data, leading to notably degraded performance. Moreover, they are more likely to fail to generate valid samples on the original pretraining task, indicating a severe loss of pretrained knowledge and catastrophic forgetting. In contrast, GeoAda benefits from the implicit regularization effeet of the adapter, which mitigates overfitting and preserves the performance of the pretrained model.
Ground Truth
Ours
Figure 4: Visualization Running trajectory
Table 3: Comparisons for short-term prediction 5 action categories of the CMU Mocap dataset. The best results are highlighted in bold. Results averaged over runs (std in App. 10.2).
reening
priintn
naking
prstrats
Trank Drutl
pritre
100
231
-16
20
190
23
24
160
226
416
01
163
351
691
81
14G
530
311
20
TN)
75.24
1.55
135
104.37 37
3.811
16.11
W691
42.65
15:00
16.3 31
36
16.14
14.51
$3.35
13.00
15.54
1:48
10:
1611
16.8
14:31
$2.55
24443
36.14
15
00.46
T177
1917
1001
11.16
11
66.36
$1.29
11:54
10
76.6
GFT [g)
15.48
31.94
$0.00
73:56
31.36
35.6
25.33
70.5
1679
1679
2633
13
23
31.38
11344
11.55
15.46
31.4
7336
31.0
15.4
55.55
5635
Gookde
15.70
33334
50.35
8554
1373
16.1
$341
682
1383
21.99
36.8
7A83
16.00
1686
$3.54
1635
2671
37.58
71,9
138
56.9
36,00
$3.50
Table 4: Comparisons for long- long-term prediction on 5 action categories of the CMU Mocap dataset. The best results are highlighted in bold. Results averaged over runs (std in App. 10.2).
scenarios
running
pretrain
walking
pretrain
basketball
pretrain
millisecond (ms)
560
1000
560
1000
560
1000
560
1000
560
1000
560
1000
Pretrnin
219.16
314.85
77.06
130.51
129.43 .3.43
212.94
77.06
130.51
143.49
223.99
77.06
130.51
Full FT
85.14
97.02
nan
nan
36.92
52.58
nam
nan
94.59
132.34
nan
nan
PARTIAL-& [12]
102.85
108.47
nan
51.36
84.72
118.82
182.88
106.84
146.27
nan
MLP-k
127.67
131.59
nan
Ban
62.97
102.34
nAn
000
107.30
149.58
nan
nan
GPF
61.92
71.42
nan
42.37
52.24
119.43
171.74
97.16
128.29
GPF-plus [6]
63.56
71.60
nan
41.31
56.47
nAn
000
104.54
130.76
104.51
155.02
GeoAda
70.22
77.22
130.17
34.52
50.49
78.12
129.97
91.03
120.35
76.94
129.81
5.3 Subgraph Control
Experimental setup. We adopt the QM9 [26] and GEOM-Drugs [1] dataset for pretraining a model for molecule generation, use the CrossDocked22020 dataset [7] for finetuning protein- ligand pair gen- eration. QM9 [26] contains 130k small molecules with atom types (H, C, N. O, F). GEOM-Drugs [1]
8

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Table 5: Summary of binding affinity and molecular properties of reference molecules and molecules generated by GeoAda and baselines. (T) (L) denotes whether larger / smaller number is preferred.
Methods
Vina Score (L) Vina Min ({)
Vina Dock (1)
High Affinity())
QED(T)
SA())
Diversity())
Arg.
Med.
Med.
Avg.
Med.
Avg.
Med.
Med.
Med.
Avg.
Med.
BGAN (25)
-6.3
21.1%
0.57
GraphBP [19)
-4.00
-4.70
14.2%
6.7%
0.43
0.45
0.49
0.48
0.79
0.78
[R1
-5.75
-5.61
-618
-5.88
-6.75
-6.62
37.9%
31.0%
0.51
0.50
0.63
0.63
0.70
0.70
PocketZMel [24]
-5.14
-4.70
-6.42
-5.82
-7.15
-6.79
48.4%
51.0%
0.56
0.57
0.74
0.75
0.69
0.71
Targethiif [o]]
-6.30
-633
-7.00
-7.1
58.1%
0.48
0.58
GeoAda (gm9))
-5.54
-6.31
-3.62
-7.64
57.4%
0.51
0.58
GenAda (Geom)
-5.54
-6.01
4.68
6.32
.7.64
.2.11
58.3%
59.3%
0.48
0.50
0.58
0.58
0.76
0.75
Reference
-8.36
6.41
6.71
6.49
-7.45
7.26
0.48
0.47
0.73
0.74
Table 6: Pensen-Shannon divergence of bond distance distributions between refer- ence and generated molecules. (L)
Table 7: Percentage of different ring sizes for reference and model generated molecules.
Ring
IGGNN
PoctetMMll
Tarpthii
Geobda (qotl)
(geon)
Beol
AR
Palr 7544
Tayebat
Gookda (yet) Gwodee (Gean)
1.7%
28.1%
29:35
0.15%
0.11%
0.11%
0,R
C-C
Ban 0,97
0.26
0.399
0.34
0.359
0.0%
15.7%
0,00%
2.85
6.7%
5.8
0.561
1.915
1.377
29.8%
16.4%
30.8%
47.2%
45.8%
C-K
11390
13331
08299
92.7%
50.7%
60.1%
2.6%
2.6%
12.1%
23.5
5-0
0.53
0.566
1187
0.77
0.357
0.35%
2.7%
5.35
4.7%
CC
0.550
0416
0.335
0.3%
0.1%
0.9%
3.8%
1.68
a large-scale dataset of 430k molecular conformers with heavy atoms, and we keep the lowest energy conformation for each molecule. Following the common setup for CrossDocked2020 [10], we obtain 100k complexes for training and 100 novel complexes for testing. Since CrossDocked2020 has different atom type configuration from QM9 and GEOM-Drugs, we limit the atom type to (H, C,
N, O, F, P. S, CI). Following [10), proteins and ligands are expressed as 3D atom coordinates and one-hot vectors containing the atom types.
Implementation. Following prior work [10], we use the Adam optimizer with a learning rate of 0.001 and B values of (0.95, 0.999). Batch size is set to 4 and gradient clipping set to 8. To balance the atom type and position losses, we scale the atom type loss by a factor of = 100.
Results. We evaluate molecular properties and molecular structures of the proposed model and basclines on target-aware molecule generation in Table 5, 6, and 7. Baseline models are trained on CrossDocked2020 under explicit protein conditioning. GeoAda matches, and in multiple cases surpasses the strongest baselines on all metrics, generating ligand molecules that maintain realistic structures, high binding affinity, comparable likeelis and sythetic accessibility. The lightweight adapter can inject subgraph (pocket) control into a broadly pretrained geometric diffusion model, achieving or surpassing task-specific baselines that rely on end-to-end training with protein context.
5.4 Ablations and Observations
Observation of the sudden convergence phenomenon Similar to the phenomenon observed in ControlNet [44], we also observe sudden convergence phenomenon in our training process. As shown in Figure 5, between step 4500 and 4700, both training loss and validation MSE drop abruptly rather than gradually. To investigate this behavior, we conducted inference using the saved checkpoints from steps 3600 and 5600, and observed a notable performance jump between steps 4400 and 4800, which corresponds to significant reductions in ADE and FDE by 68.3% and 73.4%.
Epoch Traning Loke
Validation MSE
ADE and FDE Training Stopa
Eysch Trrc Leve
4.85
T/ Netteee 5052
FD2
3.300
0.300
Train
0.22
153ice 203000
3550
4400
Figure 5: The sudden convergence phenomenon
Parameter efficiency analysis As shown in Appendix 10.3.1, we explore the impact of varying the number of equivariant zero layers. Increasing the number of trainable copy layers generally improves
9

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performance, but introduces more parameters and computational cost, revealing a trade-off between performance and efficiency. We also reported the number tunable parameters for different tuning strategies in Table 21. Except for full fine-tuning, which is substantially larger, all other methods, including GeoAda, use comparable parameter sizes.
Ablation Equivariant Zero Convolutions We evaluate variants assess the role of equivariant zero convolution: (1) replacing it with Gaussian-initialized standard convolutions, and (2) replacing each trainable copy with single convolution layer (see App. 10.3.2). Both modifications result in notable performance drops, underscoring the importance of zero initialization and structural design for stable and effective fine-tuning.
Conclusion
We present GeoAda, a parameter-efficient and SE(3)-qqivvarian adapter framework for geometric diffusion models. It enables effective adaptation to diverse geometric control tasks without modifying the pretrained backbone, preserving both performance and geometric consistency.
7 Acknlowlegdements
This project was funded in part by ARO (W911NF-21-1-01125) ONR (N00014-23-1-2159, and the CZ Biohub.
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and Introduction clearly state the main contributions, which include the proposal of GeoAda, an SE(3)-eqiivarian adapter framework for efficient fine- tuning of geometric diffusion models. The claims of geometric consistencllequivrrinne mitigation of overfitting and catastrophic forgetting, and wide applicability across diverse geometric control types and domains. These claims appear to be supported by the theoretical proofs (discussed in Section 4 and Appendix 7) and experimental results presented (Section 5).
parameter efficiency, preservation
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Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
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Appendix
8 Proof
Below is the explanation and proof of Proposition 4.1:
Proof. Since eg is SE(3) -equivrrvr by assumption, have for any h E SE(3).
co (h g') h- co'')"),, where g' C)
We consider each component:
The coupling operator f augments G, with control C in a way that respects the SE(3) structure: global controls modify features invariantly; subgraph controls are merged geometrically; frame controls concatenate along the temporal axis. Thus, f is SE(3)-equivariant,
The decoupling operator g selects a subset of nodes or frames without altering their coordi- nates. Therefore, commutes with SE(3) action: g(h G") h g(9").
Combining the above, we explicitly see that for any SE(3) defined as h(x) Rx + d, have:
g f(h (G)
(6a (h- ((G,())
g (h Ea (f(Gr,C))
g (co (f(Gr,
R (g En o f(Gr, C)) d
h (g ca f(),C))
Therefore, the composed function g o eg is SE(3) -quivaaaan.
9 More Details on Experiments
9.1 Hyper-parameten
We provide the detailed hyper-parameters of GeoAda in Table 8, We adopt Adam optimizer with betas (0.9, 0.999) and e = 10- 6, For all experiments, we use the linear noise schedule per [13] with Batart 0.02 and Bend 0.0001.
Table 8: Hyper-parameters of GeoAda in the experiments.
n_ l_layer
hidden
time_emi
T
batch_size
learning_ rate
N-body
6
128
32
1000
128
0.0001
MD
6
128
32
1000
128
0.0001
CMU Mocap
6
64
32
100
128
0.0001
9.2
Baselines
Full FT.
Full FT fully fine-tunes the pre-trained model f during downstream training. The entire model updated to fit the target task.
21

---

PARTIAL-K.
PARTIAL-K fine-tunes only the last k layers of the model f. while freezing the remaining layers. This method balances adaptability with parameter efficiency by limiting the number of updated layers.
Graph Prompt Feature (GPF).
In GPF, the pre-trained encoder f is kept frozen, and a learnable prompt vector p is injected into the input feature space. During training, only the prompt vector p and the prediction head are optimized. This method enables task adaptation through lightweight, task specific prompt without modifying the backbone model. In our implementation, we replace the original MLP head with three-layer Equivariant Geometric Trajectory Network (EGTN), which ensures the projection head maintains geometric consistency with the model.
Graph Prompt Feature-Plus (GPF-plus).
Extending GPF, this variant constructs node-wise prompt vectors using learnable basis vectors pi.....Pi and set of learnable linear weights a1..... dg. These components used to compute node-specific prompts p: via a compositional mechanism. The model f remains frozen, while prediction head 8, learnable basis vectors p andlearnable linear weights a; optimized.
Prompt-Template
We prepend a learnable prompt layer(Fquivariant Geometric Trajectory Network) to adapt new inputs the distribution seen during pretraining. following with prediction head 0.
MLP-k (EGTN-k).
This baseline freezes the entire pre-trained model f and replaces the prediction head with k-layer multilayer perceptron (MLP). To preserve equivariance in our setting, replace the MLP with an Equivariant Geometric Trajectory Network (EGTN) block. Only the EGTN-based head is trained during the downstream task.
9.3
Details of the datasets
9.3.1 Global Type Control
Pretrain Dataset The statistics of pretrained datasets on Global Type Control are presented in Table. 9.
Table 9: Pretrain Dataset statisties by Global Type.
Type
Washwindow
Directing Traffic
Basketball Signal
Pretrain
train
12126
9557
7776
29459
1342
2346
1920
test
1342
2346
1920
5588
Downstream datasets on Global Type Control are presented in Table. 10.
The statistics of the downstream datasets utilized for the models pretrained
Table 10: Downstream Datasct statisties by Global Type.
Type
Running
Walking
Jumping
Basketball
Soccer
train
245
869
1345
1044
1210
val
47
145
1008
254
264
test
145
1008
254
264
9.4 Model
9,4.1
Geometric Trajectory Diffusion Models
Unconditional Generation For unconditional generation, we model the trajectory distribution subject to SE(3)-invariance. The following theorem provides constraints for the prior and transition kernel.
22

---

Theorem 9.1. If the prior pT((x)) is
and the transition kernels P+-1 (x [2] xF ), VT E f1..... .....T T are SE(3)-equivariant, then the marginal p+(x;) at any step T E (0, [0,-.. _T) also SE(3) -i3)ainnvaia
121)
Prior in the ionillationinvariinn subspace. The prior is built on a translation-invariint subspace Xp C X, induced by linear transformation P:
P ID & ITN
TN 1TNITN)
which results a restricted Gaussian distribution supported only on the subspace, denoted (o I). and is isotropic and -invarrria To sample, one samples from (O, and projects it onto the subspace.
Transition kernel. The transition kernel is parameterized in the subspace Xp, given by: x (7)
Po x
14 7-1
where the mean function já is (O -eeuieequivariant. The function re-parameterized as:
1
77 3, Eo (x (r)
jo (x!
[T]
x
VI- at
where Eg P fo is an -0(3)-equivarian adaptation the proposed EGTN. Training and inference. The VLB is optimized for training, with the objective:
[ " Luncond E --- ||| Eø (x(X! m)]
The inference process involves projecting intermediate samples onto the subspace Xp.
Conditional Generation In conditional generation, the target distribution is SE(3) -equiv-aqa with respect to the given frames. The following theorem provides constraints for the prior and transition kernel.
Theorem 9.2. If the prior pr(xf xe (ol)) is
[T]
and the transition kernels Px-1(x!71 []] [T] xx Tely VT (1,".,, are -eq(ieeeuuvaariat,, the marginal pr xx(x!? xeTell
V7 E (0, Th is SE(3) equivarrai.
Flexible equivariant prior. We provide guideline for distinguishing feasible prior designs. The prior (u
[2dly ),I) is (E3uiqvauia if μ(x; (T is -Equivaata The mean function
u(x!"-o) serves an anchor transition geometric information from the given frames the target distribution. For instance, the anchor can be defined as:
T 1TXN K Σ
w (+) (e) c
SE
where the weights satisfy E w( =1
The weights w (f.s) are derived as:
Wr,s IN Σ..0
if < T. 1, if T
W, r.. (7 & h [Tal
l..s E RN w(t.))
II.-2 W.,
where 7 E T are learnable parameters, ensuring the constraint for translation equivariance.
Transition kernel. To match the proposed prior, modify both the forward and reverse processes. The forward process is defined as:
qxx!7 x x (Tal)
= N ;x, + V1- 3, (x
21
x,).3,1).
which ensures that ((x7 transition kernel is:
[2]
[ecl X
matches the equivariant prior x,. (proof in App. ??). The reverse
Pr (x [
[Tal) NNoo(( (( 01
,
23

---

We adopt the noise prediction objective for the reverse process, rewriting μe as:
-!!" 8, where the denoising network co is implemented as an EGTN with translation invariance, ensuring the translation equivariance of μ40-
(x
11 x
[T
7) = [
co x [Ta)
(
.7)
Vi a
Training and inference. Optimizing the VLB of our diffusion model leads to the following objective:
Leond == Bxgg xXP (- [|Ie co cx x( (T)) +)]
9.5 Evaluation Metries in the Unconditional Case
All these metrics are evaluated on set of model samples with the same size the testing set.
Marginal score is computed as the absolute difference of two empirical probability density functions. Practically, we collect the z, y, coordinates at each time step marginalized over all nodes in all systems in the predictions and the ground truth (testing set). Then we split the collection into 50 bins and compute the MAE in each bin, finally averaged across all time steps to obtain the score. Note that on MD17, instead of computing the pdf on coordinates, we compute the pdf on the length of the chemical bonds, which is clearer signal that correlates to the validity of the generated MD trajectory, since during MD simulation the bond lengths are usually stable with very small vibrations. Marginal score gives broad statistical measurement how each dimension of the generated samples align with the original data.
Classification score is computed as the cross-entropy loss of a sequence classification model that aims to distinguish whether the trajectory is generated by the model or from the testing set. To be specific, we construct dataset mixed by the generated samples and the testing set, and randomly split it into 80% and 20% subsets for training and testing. Then the model is trained on the training set and the classification score is computed as the cross-entropy on the testing set. We use I I-layer EqMotion with a classification head as the model. The classification score provided intuition on how difficult it is to distinguish the generated samples and the original data.
Prediction score is computed as the MSE loss of a train-on- www-ooo--stttccttesssteete sequence model. In detail, we train 1-layer EqMotion on the sampled dataset with the task of predicting the second half of the trajectory given the first half. We then evaluate the model on the testing set and report the MSE as the prediction score. Prediction score provides intuition the capability of the generative model on generating synthetic data that well aligns with the ground truth.
sequence to
10
More Experiments and Discussions
10.1
Molecular
Additional experimental results on the Malonaldehyde and Naphthalene are shown below:
Table 11: Comparisons for Molecular Dynamics prediction on MD17 dataset (all results reported by x x10-1). The best results are highlighted in bold. Results averaged over 5 runs
Scenarios
Malonildehyde
Naphthalene
Task
Downstream
Pretrain
Downstream
Pretrain
Metrie
ADE
FDE
ADB
FDE
ADE
FDE
ADE
FDE
Pretrain
e.235
5.189:u.02s
0.962-c.oor
1.584:a..21
1.41660.o0s
2.268 cu.uus
0.714 0.972=0.00m
FT
00.02
1.511=0.000
1.405=0.c00
2.237+0.025
0.555=0.00)
0.867+0.010
Dan
PARTIAL-& [12)
2.981+n.004
1.675=n.015
1 1.230-c.coa
2,110=a.com
0.653=a.002
0.903+a.0us
2.083++.000 1. 1.629=0.007 nan
MLP-k
0.997su.00s
1.6941u.010
1,291 _.000
2.051.n..ss
0.71810.001
0.9691u.mm
Ban
Prompt-Tem Tem
1.
1.09220.01a
2.003g0.000
2.323_0.004
3.35 1.35110.0001
0.972_0.006 006
1.593g0.021
nan
nan
GPF [6]
1.176gu.m2
1.931
24.97
0.758
1,005
go.uus
nan
nan 2.674_o
GPF-plus [6]
1.0181n.005
1.79320.010
3.527_o.001
4.71911.997
0.71710.003
0.87310.006
1.891000000
GeoAda
0.862 20.002
1.414
20.014
0.963=0.c07
1.573=0.015
0.581=0.002
0.822=0.004
0.969 007
10.2
Human Motion
Additional experimental results on the jumping and soccer scenarios are presented below. We also report the standard deviations across all experiments.
24

---

Table 12: Short-term prediction on running from the CMU Mocap dataset.
scenarios
running
pretrain
millisccond (ms)
80
160
320
400
80
160
320
400
Pretrain
28. 28.74:10.31
57.9% 10.99
126.20 10.95
159.37
7.94119.02
16.84 20.04
39.91 g0.45
$2.45
1:000
Full FT
20.34
35.26 10019
60.58
70.20
nan
nan
nun
PARTIAL-K
20.47=0.12
36.04 =0.40
68. 68.15
82.59=0.a6
nan
nan
pan
nan
MLP-&
23.35 +0.30
44.44+0.71
84.27 #1.58
101.42+2.11
nan
nan
Ban
nan 79.55 1:1:1 nan 52.61
GPF
19.17.0.08
32.8510.06
$2.83
60.90 1:154
21.38 1.0.0
35.44
65.23 Ban
GPF--puu
19.11
31.93+0.:1
49.85 #1:21
56.62=1.39
nan 4.972
Ban
GeoAda
18.70 10.37
33.56.10.25
50.26
55.54 00.35
16.91
40.06 10.06.0042
00.42
Table 13: Short-term prediction on walking from the CMU Mocap dataset.
scenarios
walking
pretrain
millisecond (ms)
80
160
320
400
80
160
320
400
Pretrain
15.4990..7
30.66620116
68.71
89.23
7.941+0.02
16.84
20.01
39.91
52.45
$0.07
Full FT
10.01 20.17
15.12 10.14
23.98
28.49 1:019
nan
nan
nan
nan
PARTIAL-K
10:47
16.97
40.43
30.97.0.00
37,69
17.26.0033 nan
31.75 nan
66.2949044
84.27=0.79 nan
MI.P&
10.86:1.07
18.74
11.57
35.78
44.86:1.33
nan
GPF
10.79
16.79 10.16
28.3220021
33.48.10.2 22
22. 22.04-10.35
37.10
=0 40 nan
71.24
88.23 nan $2. 01
GPF-plus
10.17 #0.16
16.23+0.12
26.29
31.54 10019
nan
GeoAda
8,92.1.02
13.82 26
22.99
26.68
7.932
16.9020.03
38, 38.96
Table 14: Short-term prediction comparison on the baskethall action from the CMU Mocap dataset.
scenarios
baskethall
pretrain
millisecond (ms)
80
160
320
400
80
160
320
400
Pretrain
17.9249.05
35.8920.12
18.4819.47
101.12:0 09
2.941
16.842001
39.91 10.43
52.45
FT
16.95+0.11
30.33 40.17
58, 28
71.93=0.54
PARTIAL-E
17.54:9.12
32.03=0.43
62,96.0.86
78.95
MLP-k
17.6020.50
34.76=1.26
72, 72.90
86.34 =1.50
GPF
18.48+0.00
31.94=0.14
58.80+0.2s
73.5650.29
21.38#0.11
35.44.0.27
65 65.23
a9.55
GPF-plus
17.17 #0.07
31.86:0.15
$8.48:0.52
72.71 #0.21
GeoAda
16.85
29.71=0.41
57.59
71.19
7.898
16.79
#0.05
39.70 #0.04
52.50
Table 15: Short-term prediction comparison on the jumping action from the CMU Mocap dataset.
scenarios
jumping
pretrain
millisecond (ms)
80
160
320
400
80
160
320
400
Pretrain
7,941 #0.02
16.84 #0.04
39.91 20.43
52.45=0007
FT
26.67:0.10
20.83=0.29
94.13=0.58
112.66:0.71
PARTIAL-
26.01
49.19 10.00
95.84.0.13
116.24 10.25
19.08
38.5320.34
79.77.0.22
99.85
MLP-K
22.63/man
44.68/aa
88. 93/mam
13han
15.32a0
31.9220:00
66.50.0.42
22.55
GPF
28.74 18.74
51.97=0.19
97. 27.80
117.94 #0.37
=0.08
GPP--lus
GeoAda
25.91
48.83
91.51 20.07
10.024
7.956 10.00
16.82
20.04
39.55 20.47
52.57
20.00
Table 16: Short-term prediction comparison on the soccer action from the CMU Mocap dataset.
scenarios
soccer
pretrain
millisccond (ms)
160
320
400
80
160
320
400
Pretrain
7.941=6.02
16.84
39.91 20.45
52.45.00r
FT
17.65 2017
31.43 19:35
59.7619.41
74.30 10.54
PARTIAL-S
18.83=0.10
32.86s0.07
64.58
81.53
14.1420.41
24.95
50.89
64 64.2420.51
MLP-
GPF
19.28
32.18
42
73.6349.63
15.70=0.30
28.31 +0 as
58.57
20.28
GPF-plus GeoAda
19.11
32.03
59.6749.6
74,25 20.05
15.22=0.28
26.22=0.29
52.02=0.47
65.1740.5a
17.04=0.14
30.03
53.51
64.78+.042
7.961 #0.02
+6.90
39.46 #0.41
$2.43 20.00
Table 17: Long-term prediction on CMU Mocap: Running and Walking.
scenarios
ruaning
pretrain
walking
pretrain
millisecond (ms)
500
1000
560
1000
560
1000
560
1000
Pretrain
219.16....8
314.8512.05
77.06
[30.51
129.43
212.94
77.06 11:47
130.51 10:77
Full FT
85.14 =2.30
97.02-1.45
nan
Rdn
36.92-1.57
52.58+s002
man
nan
PARTIAL-& [12)
102.85 #1.68
108.47+2.0s
nan
51.36=1.00
84.7240.67
118 82.8.20.
182.88+0.19 nan 171.74_0.55 nan 129.97 10:30
MT.P-k
127.67_3.46
131.59
nan
nan 62.97_1.45
102.3410.46
nan
GPF [6]
61. 92.92.1.00
71.42.1.327
nan
nan
42.37_n.33
52.24 1o:3s
119.43_00.0
GPF-plus
63.5621.54
71.60=0.05
nan
11.31
56.47a0.4
GeuAda
60.88 20.s2
70.22
77.22 10.45
130.17 10.36
34.52
20:00
$0.49 10:33
28.12 10.t0
25

---

Table 18: Long-term prediction CMU Mocap: Jumping and Soccer.
aceniacios
jumping
pretrain
soccer
pretrain
millisecond (mS)
560
1000
Pretrain
77.06.0.47
=30.51=0.27
77.06:0.47
130,51+027
Pull
145, 22
199.34
101.44
#0.51
157. #0.99
PARTIAL-K(12)
149. 06
18 0.52 81
135 d5
186.1621.8
113.88 20.75
170.50
89.63 21.00
142.4
184.77munn
110771
158.55
GPF 161
151,50
19.594
100.23
151884
104.03:0.st
161.56:1.31
GPF-ppus
142.30+1.12
GeoAda
139.46 20.20
18.00l
26.98
130.72
84.91a6.40
125.91 ae
77.19 =0.48
130.06:0.a1
Table 19: Long-term prediction CMU Mocap: Basketball.
scenarios
basketball
pretrain
millisecond (ms)
1000
560
1000
Pretrain
143.49=1.19
223,99
77.06+0.47
130.51+0.27
Full FT
94.59.0.5s
132.34::.300
min
mall
PAKTIAL-K(12)
106.84 +1.00
146.27
MLP-&
107 2:277
149.58::2.24
man
nall
GPF [6]
17.1620.35
088.29:0.43
GlF-plas [6]
104.54 20:20
130.76
10.55
155.02 10.51
GenAda
91.032033
120.35.0001
76.94..015
129.81
10.3 Ablations
10.3.1 Parameter efficiency analysis
As shown in Table 20, we explore the impact of varying the number of equivariant adapter blocks. Increasing the number of trainable copy layers gen- erally improves performance, but introduces more parameters and computational cost, revealing a trade- off between performance and efficiency. We have computed the number of tunable parameters for all baselines and GeoAda. The statisties are presented Table 21. Except for Full Fine-Tuning, all methods have a comparable number of tunable parameters, ensuring a fair comparison.
Table 20: Different numbers of adapter blocks
Number
ADE
FDE
1 1,321
3,088
2
1.291
2.968
3
1.108
2.621
4
1.104
2.588
5
1.106
2.686
Table 21: The number of tunable parameters for different tuning strategies.
Dataset
Tuning Strategy
Total Parameters
Tunable Parameters
Full FT
1418252 -5.41 MB
1418252 -5,41 MB
PARTIAL-K
1418252 -5.41 MB
711302 -2.71 MB
MLP-k
2125202 -8.11 MB
711302 -2.71 MB
Charged Partiele
Prompt-Ted Tem
1418252 -5.41 MB
711302 -2.71 MB
GPF
2125266 -8.11 1..11M MB
711366 -2.71 MB
GPF-plus
2125847 -8.11
711947 -2.72 MB
GeoAda
2125691 -8.11 MB
711791 -2.72 MB
Full FT
1424268 -5.43 MB
1424268 -5.43 MB
PARTIAL-k
1424268 -5.43 MB
716166 -2.73 MB
MLP-k
2132370 -8.13 MB
716166 -2.73 MB
MD17
Prompt-Tem
1424268 -5.43 MB
716166 -2.73 MB
GPF
2132434 -8.13 MB
716230 -2.73 MB
GPF-plus
2135079 -8.14 MB
718875 -2.74 MB
GeoAda
2132844 -8.14 MB
716640 -2.73 MB
Full FT
368012 -1.40 MB
368012-1.40 MB
PARTIAL-K
368012 -1.40 MB
185990-0.71 MB
MLP-k
550034 -2.10 MB
185990-0.71 MB
CMU Mocap
GPF
550098 -2.10 MB
186054 -0.71 MB
GPF-plus
553259 -2.11 MB
189215 -0.72 MB
GeoAda
550075 -2.10 MB
186031-0.71 MB
26

---

10.3.2 Ablative Architectures
We study the following ablative architectures shown in Figure 6, Figure 7, Figure 8:
Ceok
Semner
Preaeo poot
Foood
Mocal docoes
Somplh Cpp
Equceried Adigee liok
Das: .1.
Ouge: wi
Duge: MM
Figure 6: GeoAda
Figure 7: w/o zero convolution
Figure 8: w/o trainable copy
Proposed GeoAda,
The proposed architecture in the main paper.
Replacing the zero convolutions with standard convolution layers initialized with Gaussian weights.
Without Zero Convolution.
Lightweight Layers. convolution layers.
This architecture does not use trainable copy, and directly initializes single
Results We present the results of this ablative study Table 22, Table 23, Table 24 and Table 25.
Table 22: Comparisons for Molecular Dynamics prediction on MD17 dataset (all results reported by x x10=+). The best results are highlighted in bold. Results averaged over 5 runs
Scenarios
Aspirin
Benzene
Task
Downstream
Pretrain
Downstream
Pretrain
Metric
ADE
FDE
ADE
FDE
ADE
FDE
ADE
FDE
w/o trainable copy
2.232
3,501
19.022 2.197 20.007
3.449:00m
0.607
0.952
0. 0.948:2.mm
w/o zero conv
0.929
=0.002
1.619=0.00
1.203+0.009
1.975=0.01s
0,214=0.001
0.359+0.004
#0.001
0.469=0.007
GeoAAa
0.891
=0 003
10.008
1.06010.000 coa
1.852 20 002
0.191 20.000
0.319 002
0.240.0.00z
0.394
Table 23: Ablation study of Short-term prediction running from the CMU Mocap dataset.
scenarios
running
pretrain
millisccond (ms)
80
160
320
400
160
320
400
w/o trainable copy
44,52=0.44
76.98=1.20
134.91
159.75.2.45
198. 198.16=2.0
139.24
339.24-0.33
270.04-0.50
314.89=0.0s
w/o zero cony
19.07.mar
34.2510.92
51.75
55.74 15.74
nan
nan
nan
nan
GeoAda
18.70
33.56.0.2
50.261..42
55.54:...0
7.972.042
16.91.u000
40.06.n.42
22.61
Table 24: Ablation study of Short-term prediction walking from the CMU Mocap dataset.
scenarios
walking
pretrain
millisecond (ms)
320
320
400
w/o trainable copy
23.77.0.15
43.43g0.31
84.79.0.77
105.D811.25
w/o zero comv
12.6220.07
20.6720.30
36.75
44.69
18:0.12
58. 18
102. 06....
123. 82 04
GeoAda
8.9++1002
13.82+1.26
22.99=1.80
26.68=1.31
7.932=0003
16.90=0.04
38.9620.4
$2.54
Table 25: Ablation study of long-term prediction running, walking from the CMU Mocap dataset.
scenarios
running
pretrain
walking
pretrain
(ms)
1000
560
5600
1000
w/o trainable copy
198, 162.66
228.41=2.00
365.
365.41=0.5
374.74=0.48
143. 24
214.78::.22
nan
nun
wlo conv
64. 00.69-0.37
74.64=0.50
uan
60.28=1107
93.99
165. 63..868
90999900... 129.97 2:0
GeoAda
60.88 =0.90
70.22:0.00
77.22 10.45
130.17 00.30
34.52 2:
50.49 20:3
78.12 20
27

---

10.4 Standard Deviations
We have already provided the standard deviations in App. 10.2.
11 Discussion
Limitation
While GeoAda demonstrates strong empirical performance and theoretical grounding preserving -quivaquure during fine-tuning, several limitations remain: The effectiveness of GeoAda hinges the design of coupling and decoupling operators for control injection. While theoretically sound, these handcrafted designs may not generalize well to control signals with high- dimensional or structured semantics. Moreover, although GeoAda is validated across multiple domains (c.g., particles, molecules, human motion), the evaluations are limited to medium datasets and relatively small models. Assessing its scalability to larger systems such as full proteins or macromolecular essemblies-remann an important direction for future work.
28


Reviews:
[{"review_id": "ANsTxUV1MY", "reviewer": "Reviewer_P2xL", "summary": "The authors propose a novel adapter design for the parameter-efficient fine tuning of pre-trained GNN-based SE(3)-equivariant diffusion models. Their framework allows for adding new flexible conditioning signals and are designed for efficient and stable training from the proposed zero initialisation. In addition, the authors ensure that SE(3) equivariance is preserved by their adapter design.", "questions": "- It appears that Equation 7 is a bit misleading as the adapter acts on the intermediate activations of the original model $\\epsilon_\\theta$ not just the final layer. Is there any reason for why this choice of notation is used instead?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n- Address an important yet underexplored area of fine-tuning geometric diffusion models.\n- Nice, simple idea and implementation with compelling results.\n- Good range of experiments, ablations and baselines to validate the framework.\n\nWeaknesses:\n\n- The essential idea is not too novel due to prior work on ControlNet.\n\nTypos:\n\n- Line 51: missing a space in \"work(GeoAda)\"\n- Line 138: should be \"Such a feature\" instead of \"Such feature\"", "was_revised": true, "final_justification": "I believe the paper is worthy of acceptance and the authors have further addressed the points raised in the review. I will maintain my rating at 5 for acceptance.", "rebuttal": "We sincerely appreciate your positive assessment and valuable suggestions on improving our paper. Regarding your questions, we detailed our responses below.\n### ` W1. Novelty beyond ControlNet`\n\nWe agree that ControlNet is a key inspiration for our work. However, our primary contributions and novelty lie in successfully adapting and extending this paradigm to the geometric deep learning domain which is non-trivial. Our core technical innovations include:\n* Designing domain-specific coupling/decoupling operators that can inject diverse geometric conditions (e.g., global, subgraphs, Frame control) into a pre-trained model.\n* Ensuring the adapter architecture is equivariant, which is a fundamental requirement for most geometric tasks and not an aspect of the original ControlNet.\n* Demonstrating the versatility of this approach across varied and important geometric tasks like particle /molecular dynamics, human motion, and molecular generation.\nWe will restructure the introduction and related work sections to more explicitly disentangle our contributions from ControlNet and highlight the unique challenges and solutions for geometric data.\n\n### ` W1.Typos`\nThank you for your careful review and for pointing out these typos. We will correct the two errors you mentioned in Lines 51 & 138 in the camera-ready version. We will also thoroughly check the rest of the manuscript to ensure no similar issues remain.\n\n### `Q1. Notation in Eq. (7)`\nThank you for this insightful question. You are correct that our adapter acts on intermediate activations, not just the final layer, as shown in Figure 2, where the adapter $s_{\\theta', \\phi} $ processes the control $ \\mathcal{C} $ in addition to the original inputs $ (\\mathcal{G}_\\tau, \\tau) $.\n\nWe use the notation in our loss function to express the high-level training objective in a clear and compact way: \nThis formula defines the overall goal, training the adapter $ s_{\\theta', \\phi} $ to produce a corrective signal that is added to the frozen model’s $ \\epsilon_\\theta $ prediction.  \nThe layer-by-layer additions in our architecture are the concrete mechanism to achieve this high-level objective.\n\nWe acknowledge this distinction could be clearer and will revise Section 3.2  to explicitly connect the objective function with its layer-wise architectural implementation.\n\n\n## **Summary**\nWe hope our answers address your concerns. Thanks again for recognizing our contribution to this important and challenging topic, as well as the effectiveness of our approach and the comprehensiveness of our evaluation."}, {"review_id": "Tl1ahx0V4y", "reviewer": "Reviewer_iYKL", "summary": "This paper introduces GeoAda, a framework for adapting pre-trained geometric diffusion models for conditional generation by learning adapter blocks on top of the frozen pre-trained model. GeoAda is conceptually similar to the ControlNet architecture [1], which was developed for controlling text-to-image diffusion models, and extends it to the geometric domain by designing SE(3)-equivariant adapter blocks. GeoAda covers different control types and shows promising experimental results across a variety of tasks.", "questions": "1. In subgraph control, can the control signal be part of the graph itself (and not a separate graph as in the pocket-conditioned example)? For example, can you condition on a scaffold of a molecule and complete the rest? If yes, how does this fit into the proposed framework?\n2. In global type control, how is the MLP in the coupling operator $f$ trained? Is it jointly trained with the rest of the model? Also, line 149 says \"linear\" transformation, which is not correct if an MLP is used (assuming it has some non-linearities).\n3. How exactly do you select the trainable copy for fine-tuning? How is \"selecting the first layer for every K consecutive layers from the pretrained model\" actually implemented?\n4. Can you combine multiple adapters, as in ControlNet? Can you also combine them if they are independently trained? For example, one might want to condition on a protein pocket and a target property at the same time.\n5. Equation (6) uses $\\phi_h \\cdot h_i$, where $\\phi_h \\in \\mathbb{R}^H$, which seems inconsistent. Should $\\phi_h$ be a scalar, or should the multiplication be an element-wise product?\n6. In the results tables, what does \"nan\" refer to? And in Table 1, what does \"-\" refer to?\n\n**References**\n\n[1] Zhang, Lvmin, Anyi Rao, and Maneesh Agrawala. \"Adding conditional control to text-to-image diffusion models.\" Proceedings of the IEEE/CVF international conference on computer vision. 2023.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n* The problem of adapting pre-trained geometric diffusion models to different downstream tasks is interesting and has many real-world applications.\n* The paper is well-written with a clear structure and presentation.\n* The proposed method is well-motivated and technically sound.\n* The experiments cover a wide range of applications and show the good performance of the proposed method.\n\n**Weaknesses**\n\n* The core idea of the paper is taken from the ControlNet architecture [1], which limits the novelty aspect of the paper. However, the paper successfully adapts it to the geometric domain by designing adequate coupling and decoupling operators and ensuring the adapter block is equivariant. The authors should clearly highlight their own contributions and disentangle them from prior work.\n* Some details about the experimental setups are not clear, which makes it hard to interpret the results. For example, it is not clear which model architecture is used for each task, and how the trainable copy is selected from the pre-trained model. Also, the human pose estimation experiments are not clear (what is the input/output of the model?, how do you choose the joints?)", "was_revised": true, "final_justification": "The authors clearly answered my questions. However, while the paper nicely adapts the ControlNet architecture to the geometric domain, the core idea is similar. Therefore, I maintain my score of 4.", "rebuttal": "We sincerely appreciate your positive assessment and valuable suggestions on improving our paper. Regarding your questions, we detailed our responses below.\n### `W1. Novelty beyond ControlNet`\nWe agree that ControlNet is a key inspiration for our work. However, as the reviewer also mentioned, our primary contribution and novelty lie in successfully adapting and extending this paradigm to the geometric deep learning domain which is non-trivial. Our core technical innovations include:\n* Designing domain-specific coupling/decoupling operators that can inject diverse geometric conditions (e.g., global, subgraphs, Frame control) into a pre-trained model.\n* Ensuring the adapter architecture is equivariant, which is a fundamental requirement for most geometric tasks and not an aspect of the original ControlNet.\n* Demonstrating the versatility of this approach across varied and important geometric tasks like particle /molecular dynamics, human motion, and molecular generation.\n\nWe will restructure the introduction and related work sections to more explicitly disentangle our contributions from ControlNet and highlight the unique challenges and solutions for geometric data.\n### `W2. Experimental Details`\nWe sincerely apologize for the lack of clarity regarding experimental details in the main paper and will revise the manuscript to include a more thorough description.\n\n**Model Architectures & Trainable Copy Strategy:**\n\n For both trajectory control and global control settings, we follow the same setup as GeoTDM [1]. The backbone model used in our method is EGTN, which is also employed for all baselines to ensure fair comparison. The original base model consists of six EGTN layers. We insert three trainable copies at layers 1, 3, and 5. That is, the model architecture becomes:\n```\ninput → layer1_origin + layer1_copy → layer2_origin → layer3_origin + layer3_copy  \n→ layer4_origin → layer5_origin + layer5_copy → layer6_origin → output.\n```\nFor subgraph control, the base model is following the setting of TargetDiff [2], which has nine layers in total. We apply the same strategy by inserting trainable copies at layers 1, 3, 5, and 7.\n\nWe further perform an ablation study on the number of trainable copy layers in Section 5.4 and Appendix 9.3.1 (Table 20). The results show that increasing the number of trainable layers generally improves performance, but also leads to higher parameter count and computational cost, revealing a trade-off between accuracy and efficiency.\n\n**Human Motion**\n\nThe Human Mocap dataset is a widely adopted benchmark for human pose prediction. Due to space limitations, the detailed dataset splits and experimental setup for our human motion experiments are provided in Appendix 8.3.1. For the input/output formats and joint selection, we closely follow the configuration used in MSR-GCN [3], taking in 10 Frames and predicting the following 25 frames.\n\nWe sincerely thank the reviewer for pointing out these sources of confusion. In the revised version of the paper, we will explicitly reference both this appendix section and the relevant prior work in the main text to enhance clarity and improve accessibility for readers.\n\n[1] Geometric trajectory diffusion models.\n\n[2] 3d equivariant diffusion for target-aware molecule generation and affinity prediction. \n\n[3] MSR-GCN: Multi-Scale Residual Graph Convolution Networks for Human Motion Prediction\n\n### ` Q1. Subgraph Control`\nThank you for raising this interesting question. In the case that the subgraph control $ \\mathcal{C} $ is part of the graph $ \\mathcal{G} $ itself, we can instead implement the coupling operator f as an identity function since the original graph is already a supergraph of the subgraph control. For the decoupling operator, we can keep it the same that extracts the nodes that need to optimize from the output of the model and discards the nodes in the subgraph control $ \\mathcal{C}$.\n\n### ` Q2. Global type Control`\nYes, the coupling function $f$ is trained together with the rest of the model. In line 150 we introduce $ f $ as an MLP as a general case, while we practically find that a simple linear layer already works well enough for $ f $ thus having kept such a design. We will clarify this point in the final version.\n### ` Q3. Selection of Trainable copies`\nAs mentioned in W2, \n```\ninput → layer1_origin + layer1_copy → layer2_origin → layer3_origin + layer3_copy  \n→ layer4_origin → layer5_origin + layer5_copy → layer6_origin → output. \n```\nis an example of selecting the first layer of every K=2 layers. We will incorporate the corresponding clarifications into the main text in the revised version.\n\n### ` Q4. multiple adapters`\nYes, GeoAda is able to combine multiple adapters which are separately trained by composing the corresponding scores $\\mathbf{s}_\\theta$ produced by the adapters together during sampling. \n\nTo demonstrate such potential, we provide an additional experiment on motion capture dataset by separately training two adapters that correspond to frame control (for additional 5 frames) and global type control (following our setup in Sec 5.2), respectively. The model successfully generates prolonged simulation on the new motion (running) with results of 19.10, 33.63, 50.38, 55.92, 61.13, 71.34 on 80 160 320 400 560 1000ms, showcasing its strong generalization towards composing different controls.\n### `Q5. Equation (6)`\nThank you for pointing out the ambiguity in Equation (6). We confirm that $\\phi_h$ is a vector, and the use of the dot symbol “$\\cdot$” was a typo. The intended operation is element-wise multiplication, and we will correct the symbol to “$\\odot$” in the final manuscript to ensure clarity. \n### ` Q6. nan & –`\nThank you for pointing out this confusion.\n\n“NaN” indicates that the model experienced generation collapse and failed to produce valid outputs due to numerical instability. This issue was observed in certain baseline models after fine-tuning, particularly when evaluated on the original task, where they were unable to generate numerically valid samples. This further highlights the necessity of our method, which preserves stability and avoids such collapse. \n\nThe “–” in Table 1 for Prompt-Tem under the unconditional setting denotes that this baseline is not applicable. Prompt-Tem is specifically designed to match a known conditioning frame (e.g., frame 5 to frame 10), and thus cannot be meaningfully applied to unconditional generation scenarios where no such conditioning exists.\n\nWe sincerely thank the reviewer for pointing out the lack of explanation for these two cases. In the revised version, we will update the caption of Table 1 as follows to provide a clearer description:\n```\nTable 1. Comparisons on the CHARGED PARTICLES dataset (all results reported as ×10⁻¹). (↑)/(↓) indicates whether a higher/lower value is preferred. “NaN” denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on original task. “–” indicates that the baseline Prompt-Tem requires explicit conditioning and cannot be applied when no conditioning frame is given.\n```\n## Summary\nWe hope our answers sufficiently address your concerns regarding: (1) Novelty Clarification, (2) Experimental Details,(3) Subgraph Control Integration, (4) Global Control MLP Training, (5)Trainable Copy Selection,(6) Multiple Adapter Composition, (7) Equation. 6 Notation, and (8)“NaN” and “–” Clarification.\n\nWe also sincerely thank the reviewer for the positive feedback on both the technical soundness of our approach and the breadth of our experimental validation. We truly appreciate your reconsideration of our work in light of our responses. Thank you once again for your valuable insights."}, {"review_id": "X9oKTXvUKN", "reviewer": "Reviewer_TDhS", "summary": "This paper presents GeoAda, an SE(3)-equivariant adapter framework for efficient fine-tuning of geometric diffusion models under diverse geometric conditions. GeoAda integrates lightweight, plug-in adapters into a frozen pretrained denoiser, using coupling/decoupling operators, selectively trainable layers, and zero-initialized equivariant convolutions for stable optimization. It preserves SE(3)-equivariance and achieves strong transfer performance across tasks like dynamics simulation and molecule generation, outperforming or matching full fine-tuning while reducing overfitting and forgetting.", "questions": "1. In Table 1, the metrics \"Marg, Class, and Pred\" should be introduced more clearly in the main text rather than only in the appendix. Providing brief descriptions upfront would improve clarity and help readers better interpret the results.\n2. The presence of numerous \"NaN\" results in the experiments raises concerns. It would be helpful to clarify the underlying reasons for these failures, particularly in relation to the specific baselines, to provide a more complete and transparent evaluation.\n3. What specific pretrained model is used for each task? This information seems to be missing—could the authors clarify it to improve transparency and reproducibility?\n4. In the \"task\" row of the table, it’s recommended to replace \"FT\" with \"Downstream\" to avoid potential confusion and improve clarity.\n5. Why doesn’t the Subgraph Control setting include results on the original (pretrain) task? Including them would help assess whether control fine-tuning preserves or compromises performance on the base task.\n\n**Note**: I will raise my score if the authors solve my concerns.", "limitations": "As mentioned in the **Weakness** part, the method may fail in out-of-distribution (OOD) settings, which are critical in real-world applications. Could the authors explore ways to improve the approach under OOD scenarios? Addressing this limitation would significantly strengthen the paper's contribution.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "### Strengths\n1. The inability of existing geometric diffusion models to efficiently adapt to new geometric control tasks is convincingly argued, addressing a key pain point for real-world applications.\n2. The method is well-motivated, with sound theoretical backing. The authors provide a proof  that their adapter construction retains SE(3)-equivariance, an essential property for geometric models.\n3. GeoAda offers an architecture-agnostic mechanism to inject control into geometric diffusion models using equivariant adapters, drawing inspiration from image diffusion adapters but thoughtfully extending them to the geometric (3D) and equivariant setting.\n4. Experiments span a diverse set of domains. The results consistently show that GeoAda matches or outperforms strong baselines (such as full fine-tuning, prompt and head-only tuning) across frame, global, and subgraph control tasks. Notably, in Table 5 and Table 6, key molecular property metrics and distributional metrics demonstrate superior or competitive performance.\n\n### Weaknesses\n1. While the method claims that choosing which layers to copy/introduce adapters into can matter for effectiveness (Section 4.3), there is insufficient discussion in the main paper on how sensitive results are to these architectural decisions. More quantitative results  regarding how the choice of adapter positions, number of inserted blocks, and their impact on expressivity/regularization would strengthen the argument.\n2. The paper emphasizes parameter efficiency but provides only minimal quantitative analysis of actual wall-clock training time, memory usage, or scalability to very large models. A more detailed treatment—with explicit profiling, speedup ratios, or resource consumption figures for different settings—would be informative to practitioners.\n3. The experimental section covers several domains, but does not fully assess the adapter’s robustness to transfer across out-of-distribution (OOD) controls or tasks, e.g., how performance degrades if the new task features significantly different structural characteristics than seen during pretraining.\n4.  While Figures 1 and 2 effectively clarify the architecture, more qualitative or structural analysis of what the adapters actually learn (e.g., via feature attribution or intermediate representation visualization) could provide deeper insights.", "was_revised": true, "final_justification": "The authors have addressed my concerns regarding the ablation experiments. As a result, I have increased my recommendation score from 3 to 4, and my confidence level from 2 to 4.", "rebuttal": "Thank you for your detailed review and valuable feedback. We have addressed your concerns below and hope these clarifications will assist you in re-evaluating and update the score:\n\n### ` W1. Sensitive Results`\nThank you for pointing this out — this is indeed an important aspect. To better quantify the impact of architectural choices, we’ve conducted ablation study on the number of trainable copy layers, reported in Section 5.4 and Appendix 9.3.1 (Table 20). The results show that increasing the number of trainable layers generally improves performance, but also introduces additional parameters and computational cost, highlighting a trade-off between accuracy and efficiency.\n\nWe further ablated the architectural design of our adapters in Section 5.4 and Appendix 9.3.2. Specifically, we evaluated two variants to assess the role of the equivariant zero convolution: (1) replacing it with standard Gaussian-initialized convolutions, and (2) replacing each trainable copy block with a single convolution layer. Both modifications resulted in noticeable performance degradation, emphasizing the importance of zero initialization and the proposed structural design for stable and effective fine-tuning.\n\nWe apologize for not presenting these results more clearly in the main paper due to space limitations. In the revised version, we will include key tables and results in the main text to improve clarity and visibility.\n\n### ` W2. Usage details`\nWe apologize for the confusion, and we completely agree that parameter analysis is important. As mentioned in Section 5.4, we report the number of tunable parameters for different tuning strategies in Appendix 9.3, Table 21. Specifically, Full Fine-Tuning involves 1,418,252 tunable parameters (\\~5.41 MB), whereas GeoAda only requires 711,791 tunable parameters (~2.72 MB), effectively reducing the parameter count by half. Despite this reduction, GeoAda achieves better or comparable performance on downstream tasks while also preserving performance on the original task,  avoiding issues such as model forgetting or collapse. \nWe will make sure to highlight this quantitative analysis more clearly in the main text of the revised version.\n\n### ` W3. OOD result`\nEvaluating robustness to OOD controls is indeed a valuable aspect. We further evaluate our model on OOD task involving frame control on Charged Particle setting conditioning on 5 frames to predict the next 20 frames.\n\n|                | OOD task 5          |                  | Downstream task 15 |                    |      Pretrain task 10 |                  |\n|:----------------:|:----------------------:|:------------------:|:------------------------:|:------------------:|:--------------------------:|:------------------:|\n|                | ADE                  | FDE              | ADE                    | FDE              | ADE                      | FDE              |\n| **Base**       | 12.1955±0.089*   | 20.8427±0.247| 11.826±0.133      | 20.395±0.249 | 1.177±0.018         | 2.815±0.037 |\n| **SFT**        |   338.02   ± 4.36    |   340.74   ± 4.42        | 1.106±0.007            | 2.590±0.040      | 5.998±0.041              | 11.75±0.107      |\n| **GeoAda**   | 1.0771±0.005        | 2.3864±0.022     | 1.105±0.012            | 2.621±0.033      | 1.175±0.033              | 2.806±0.033      |\n\nThese results highlight the strong OOD generalization and downstream performance of GeoAda.\n\n### ` W4. Feature`\nThank you for this suggestion. To provide deeper insight into the behavior of the adapters, we generated visualizations comparing the outputs of the original (frozen) network, the trainable copy, and the ground truth during inference. These comparisons help illustrate how the adapter modifies the generation trajectory and captures control-relevant structures. Due to the rebuttal policy restricting figures, we are unable to include these results here, but we will incorporate them in the camera-ready version to support a more comprehensive understanding of the model's effect.\n\n### ` Q1. Metrics Descriptions in Main Paper`\nWe fully agree that these metrics should be better introduced in the main text to offer more background for the reader. In the revised version, we will include the following concise explanation of “Marg,” “Class,” and “Pred” in Section 5.1 to improve readability and facilitate interpretation of the results:\n```\nThe Marginal score measures statistical alignment by computing the mean absolute error (MAE) between binned distributions of model-generated and ground-truth coordinates (or bond lengths for MD17). The Classification score is the cross-entropy of a binary classifier trained to distinguish generated trajectories from real ones, offering insight into sample realism. The Prediction score measures the mean squared error (MSE) of a sequence model trained on generated data and tested on real trajectories, reflecting the utility of generated samples for downstream prediction.  For more detailed metric definitions, please refer to Appendix 8.5.\n```\n### ` Q2. NaN `\n“NaN” indicates that the model experienced generation collapse and failed to produce valid outputs due to numerical instability. This issue was observed in certain baseline models after fine-tuning, particularly when evaluated on the original task, where they were unable to generate numerically valid samples. This further highlights the necessity of our method, which preserves stability and avoids such collapse. \nWe sincerely thank the reviewer for pointing out the lack of explanation for these two cases. In the revised version, we will update the caption of Table 1 as follows to provide a clearer description:\n```\nTable 1. Comparisons on the CHARGED PARTICLES dataset (all results reported as ×10⁻¹). (↑)/(↓) indicates whether a higher/lower value is preferred. “NaN” denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on the original task. “–” indicates that the baseline Prompt-Tem  requires explicit conditioning and cannot be applied when no conditioning frame is given.\n```\n\n### ` Q3. Backbone & Pretrained Model`\nWe sincerely apologize for the lack of clarity regarding experimental details in the main paper and will revise the manuscript to include a more thorough description.\n\nFor both frame control and global control settings, we follow the same setup as GeoTDM [1]. The backbone model used in our method is EGTN, which is also employed for all baselines to ensure fair comparison. The original base model consists of six EGTN layers. We insert three trainable copies at layers 1, 3, and 5. That is, the model architecture becomes:\n```\ninput → layer1_origin + layer1_copy → layer2_origin → layer3_origin + layer3_copy  \n→ layer4_origin → layer5_origin + layer5_copy → layer6_origin → output.\n```\nFor subgraph control, the base model is following the setting of TargetDiff [2], which has nine layers in total. We apply the same strategy by inserting trainable copies at layers 1, 3, 5, and 7.\n\n[1] Geometric trajectory diffusion models.\n\n[2] 3d equivariant diffusion for target-aware molecule generation and affinity prediction. \n\n### ` Q4. Change FT with  Downstream`\nThank you for this valuable suggestion to improve clarity! We will replace “FT” with “Downstream” in all tables in the revised version.\n### ` Q5. Subgraph Control on Pretrain`\nOn the subgraph control task, all baseline methods are trained from scratch on the downstream CrossDocked dataset with protein pocket conditions. In contrast, our method is first pretrained on unconditional datasets (QM9 and GEOM-Drugs) and then fine-tuned on the downstream task, demonstrating GeoAda’s effectiveness and generalizability. Therefore, we do not report baseline performance on QM9 or GEOM-Drugs. However, this does not affect our conclusions, as our method is designed to preserve performance on the pretraining dataset while enabling effective adaptation to new tasks.\n\n## Summary\nWe hope our answers sufficiently address your concerns regarding: (1) Sensitive study Results, (2) Parameter Efficiency, (3) OOD Robustness, (4) Adapter Behavior Visualization, (5) Metric Descriptions, (6) “NaN” Clarification, (7) Pretrained Backbone and Architecture, (8) Table Label Clarity, and (9) Subgraph Control results on pretrain.\n\nWe also sincerely thank the reviewer for the positive feedback on the motivation, theoretical soundness, and practical relevance of our method, as well as the recognition of our strong and diverse experimental results. We truly appreciate your reconsideration of our work in light of our responses. Thank you once again for your valuable insights."}, {"review_id": "IPZFBavjHZ", "reviewer": "Reviewer_CvDD", "summary": "This paper introduces a framework for parameter-efficient finetuning of geometric generative models for downstream tasks that require geometric controls. It proposes an equivariant adapter formulation that is instantiated for 3 types of control inputs: global type control, subgraph control and frame control. A wide range of experiments on particle dynamics simulation, molecule dynamics, pose estimation and docking show favorable results compared to other finetuning approaches.", "questions": "1. Can the control types be combined in multi-objective settings where both a global graph property and a subgraph is to be optimized / conditioned?\n2. Why did the authors not include recent baselines such as [2], [3], [4] in the experimental evaluation for section 5.3?\n3. Can the authors discuss why finetuning for a specific task is favorable compared to training-free conditioning methods such as e.g. (classifier) guidance (as e.g. discussed in [3])?\n\n\n[2] Guan J, Zhou X, Yang Y, Bao Y, Peng J, Ma J, Liu Q, Wang L, Gu Q. DecompDiff: diffusion models with decomposed priors for structure-based drug design. arXiv preprint arXiv:2403.07902. 2024 Feb 26.\n\n[3] Ayadi, Sirine, et al. \"Unified guidance for geometry-conditioned molecular generation.\" Advances in Neural Information Processing Systems 37 (2024): 138891-138924.\n\n[4] Huang Z, Yang L, Zhou X, Zhang Z, Zhang W, Zheng X, Chen J, Wang Y, Cui B, Yang W. Protein-ligand interaction prior for binding-aware 3d molecule diffusion models. InThe Twelfth International Conference on Learning Representations 2024.", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths\n- the paper is well-motivated and the framework is introduced concisely and clearly.\n- the control types are well-presented and cover the most important control inputs in the geometric domain\n- the performance of the presented approach compared to other fine-tuning baselines is favorable\n\n## Weaknesses\n- the presentation of the contributions is clear and helpful, but is repeated several times throughout the paper. Paragraph 3 and 4 of the Introduction are rather similar, it would help the presentation if the content of those paragraphs is separated more clearly. The final paragraph of Chapter 4 only restates what is mentioned in the introduction and could be significantly shortened.\n- while the experimental results look promising and speak for the approach, the presentation of the results needs to be improved. Descriptions for Fig 2, Fig 3, Table 2 do not sufficiently explain the contents of the figures/tables. The background specifically for Tables 6 and 7 is missing; the metrics used in these experiments need introduction/explanation and the overall motivation for these evaluations should be explicitly stated. Highlighting in Table 6 and 7 is missing.\n- the related work for geometric diffusion models is sparse and can be extended to give a more complete overview over the literature. EDM ([12] in paper) is mentioned in the introduction but not presented in the related work, neither are more recent works in this line (see [1]). The authors could also consider presenting the relevant baselines from the experimental section (e.g. 5.3 TargetDiff, etc.) here.\n- (minor) typos: 121 \"are present\"? Table 1 \"dataset.\", 267 'task.\"', 312 \"use and the\"\n\n[1] Wang L, Song C, Liu Z, Rong Y, Liu Q, Wu S. Diffusion Models for Molecules: A Survey of Methods and Tasks. arXiv preprint arXiv:2502.09511. 2025 Feb 13.", "was_revised": true, "final_justification": "My remaining concerns have been addressed in the rebuttal and I can recommend acceptance. The concerns of other reviewers have also been sufficiently discussed.", "rebuttal": "### ` W1. Rewrite`\nWe sincerely thank the reviewer for recognizing the contributions of our work and for the constructive feedback on the writing. We will revise the paper to improve its overall flow and conciseness, and will significantly shorten the final paragraph of Section 4 to avoid redundancy.\n### ` W2.Table/Figure’s Descriptions`\nWe sincerely thank the reviewer for their positive feedback on our experimental results and the effectiveness of our method. We also apologize for the lack of detail in the current figure and table presentations. In the revised version, we will update their captions as follows to provide a clearer and more informative description:\n```\nFigure2. Overall framework of GeoAda. A control signal C\\mathcal{C}C is injected into the noised graph Gτ\\mathcal{G}_\\tauGτ​ and processed by an equivariant adapter block. The adapter output is added to the frozen denoiser and repeated B times to produce the final symmetry-preserving output.\n```\n```\nFigure3.  Visualization results of our GeoAda on Malonaldehyde and Naphthalene from the MD17 dataset.\n```\n```\nTable2. Comparisons for Molecular Dynamics prediction on MD17 dataset (all results reported by ×10−1 ). The best results are highlighted in bold. Results averaged over 5 runs. “NaN” denotes generation collapse due to numerical instability, typically observed in baseline models after fine-tuning on the original task. \n```\nWe will also  include the following concise explanation of “Marg,” “Class,” and “Pred” in Section 5.1 to improve readability and facilitate interpretation of the results:\n```\nThe Marginal score measures statistical alignment by computing the mean absolute error (MAE) between binned distributions of model-generated and ground-truth coordinates (or bond lengths for MD17). The Classification score is the cross-entropy of a binary classifier trained to distinguish generated trajectories from real ones, offering insight into sample realism. The Prediction score measures the mean squared error (MSE) of a sequence model trained on generated data and tested on real trajectories, reflecting the utility of generated samples for downstream prediction.  For more detailed metric definitions, please refer to Appendix 8.5.\n```\nFor Tables 6 and 7, we mainly follow the evaluation metrics used in TargetDiff. We apologize for not elaborating on them in the main text due to space limitations. In the revised version, we will include detailed descriptions in the appendix.\n\n### ` W3. Related work`\nWe thank the reviewer for this feedback. In the camera-ready version, we will expand the related work section to provide more comprehensive coverage of the literature. For the works you mentioned, we will include descriptions such as: \"EDM introduced an SE(3)-equivariant framework for 3D molecule generation that significantly improved sample quality\" and \"TargetDiff further extended these models to structure-based drug design by generating molecules conditioned on protein targets through an SE(3)-equivariant processor.\"\n\n### ` W4. Typo ` \nThank you for your careful review and for pointing out these typos. We will correct the two errors you mentioned in Lines121& 267 & 312 in the camera-ready version. We will also thoroughly check the rest of the manuscript to ensure no similar issues remain.\n\n### ` Q1.Multiple Adapters`\nYes, GeoAda is able to combine multiple adapters which are separately trained by composing the corresponding scores $\\mathbf{s}_\\theta$ produced by the adapters together during sampling. To demonstrate such potential, we provide an additional experiment on motion capture dataset by separately training two adapters that correspond to frame control (for additional 5 frames) and global type control (following our setup in Sec 5.2), respectively. The model successfully generates prolonged simulation on the new motion (running) with results of 19.10, 33.63, 50.38, 55.92,61.13,71.34 on 80 160 320 400 560 1000ms, showcasing its strong generalization towards composing different controls.\n\n### ` Q2.Recent Baseline`\nThank you for raising this. These are highly relevant and timely papers that appeared concurrently with our work. Based on the results reported in these two papers, we summarize the key numbers as follows: \n\nTable 5: Summary of binding affinity and molecular properties of reference molecules and molecules generated by GeoAda and baselines.\n\n| Methods | Vina Score (↓) | Vina Min (↓) | Vina Dock (↓) | High Affinity (↑) | QED (↑) | SA (↑) | Diversity (↑) |\n| ---------------- | ----------------- | ----------------- | ----------------- | ----------------- | --------------- | --------------- | --------------- |\n| | Avg. / Med. | Avg. / Med. | Avg. / Med. | Avg. / Med. | Avg. / Med. | Avg. / Med. | Avg. / Med. |\n| liGAN \\[22] | - / - | - / - | -6.33 / -6.20 | 21.1% / 11.1% | 0.39 / 0.39 | 0.59 / 0.57 | 0.66 / 0.67 |\n| GraphBP \\[16] | - / - | - / - | -4.80 / -4.70 | 14.2% / 6.7% | 0.43 / 0.45 | 0.49 / 0.48 | 0.79 / 0.78|\n| AR \\[18] | -5.75 / -5.64 | -6.18 / -5.88 | -6.75 / -6.62 | 37.9% / 31.0% | 0.51 / 0.50 | 0.63 / 0.63 | 0.70 / 0.70 |\n| Pocket2Mol \\[21] | -5.14 / -4.70 | -6.42 / -5.82 | -7.15 / -6.79 | 48.4% / 51.0% | 0.56 / 0.57 | 0.74 / 0.75 | 0.69 / 0.71 |\n| TargetDiff \\[8] | -5.47 / -6.30 | -6.64 / -6.83| -7.80 / -7.91 | 58.1% / 59.1% | 0.48 / 0.48 | 0.58 / 0.58 | 0.72 / 0.71 |\n|DecompDiff| -5.67 -6.04| -7.04 -7.09| -8.39 -8.43| 64.4% 71.0% |0.45 0.43 |0.61 0.60| 0.68 0.68 |\n| IPDIFF |-6.42 -7.01 |-7.45 -7.48 |-8.57 -8.51 |69.5% 75.5% |0.52 0.53| 0.61 0.59 |0.74 0.73|\n| GeoAda (qm9) | -5.54 / -6.31| -6.46 / -6.46 | -7.62 / -7.64 | 57.4% / 58.2% | 0.49 / 0.51 | 0.58 / 0.58 | 0.74 / **0.75** |\n| GeoAda (Geom) | -5.54 / -6.01| -6.68 / -6.32 | -7.64 / -7.71 | 58.3% / 59.3% | 0.48 / 0.50 | 0.58 / 0.58 | 0.76 / 0.75 |\n| Reference | -6.36 / -6.41 | -6.71 / -6.49 | -7.45 / -7.26 | - / - | 0.48 / 0.47 | 0.73 / 0.74 | - / - |\n\nTable 6: Jensen-Shannon divergence of bond distance distributions between reference and generated molecules.\n\n| Bond | liGAN | AR    | Pocket2Mol | TargetDiff | DecompDiff|IPDIFF | GeoAda (qm9) | GeoAda (Geom) |\n| ---- | ----- | ----- | ---------- | ---------- | ------------ | ------------- | ------------ | ------------- |\n| C–C  | 0.601 | 0.609 | 0.496      | 0.369  |0.359| 0.386    | 0.243   | 0.269         |\n| C=C  | 0.665 | 0.620 | 0.561      | 0.505   |  0.537 | 0.245  | 0.377    | 0.393         |\n| C–N  | 0.634 | 0.474 | 0.416      | 0.363   |   0.344  |0.298  | 0.363    | 0.396         |\n| C=N  | 0.749 | 0.635 | 0.629      | 0.550   | 0.584  |0.238   | 0.300    | 0.299    |\n| C–O  | 0.656 | 0.492 | 0.454      | 0.421 |  0.376  |0.366    | 0.418   | 0.428         |\n| C=O  | 0.661 | 0.558 | 0.516      | 0.461    | 0.374  |0.353   | 0.279    | 0.257         |\n| C\\:C | 0.497 | 0.451 | 0.416      | 0.263     | 0.251 | 0.169  | 0.305    | 0.335         |\n| C\\:N | 0.638 | 0.552 | 0.487      | 0.235  | 0.269  |0.128| 0.297        | 0.330         |\n\nTargetDiff trains molecular generation simply conditioned on protein, and there is future work, such as IP-Diff that  further adds protein and molecule interaction as additional conditions. Our work builds on the TargetDiff pipeline, taking off the protein condition during pretraining and adding trainable copy layers for Finetuning, which is the key reason why we mainly compared our result with TargetDiff and may not outperform the latest SOTA methods in every dimension. \n\nBut GeoAda consistently improves upon TargetDiff, demonstrating the effectiveness and generality. Moreover, GeoAda is modular by design and can be easily applied to other backbones, making it broadly applicable across future geometric diffusion models.\n\n\n### `Q3. FT vs Unified guidance`\nWe appreciate the reviewer for bringing this up — this is an insightful comparison and a key point that reinforces the motivation of our method.\nWhile methods like classifier guidance can offer strong control, they typically require training a separate predictor for each property and rely on adversarial gradients during sampling.This restricts their applicability to tasks lacking reliable property-specific classifiers and makes the generation process more prone to instability introduced by adversarial optimization.\n\nIn contrast, our fine-tuning approach employs lightweight, easily pluggable adapters without requiring additional predictors. These adapters also provide implicit regularization, reducing reward hacking risks and ensuring stable control. Moreover, our method generalizes effectively across diverse tasks—including frame, global, and subgraph control—where training-free methods may fall short.\n\nNonetheless, we acknowledge that both fine-tuning and guidance are complementary and promising directions. The choice between them may depend on the specific requirements of the target task.\n\n## Summary\nWe hope our responses sufficiently address your concerns regarding: (1) Writing Redundancy and Clarity, (2) Table and Figure Presentation, (3) Metric Definitions, (4) Related Work Coverage, (5) Minor Typos, (6) Multi Control Composition, (7) Inclusion of Recent Baselines, and (8) Fine-Tuning vs. Training-Free Guidance.\n\nWe sincerely thank the reviewer for recognizing the clarity of our framework, the relevance of our control settings, and the strong empirical performance across tasks. We truly appreciate your reconsideration of our work in light of our responses. Thank you again for your valuable and thoughtful feedback."}]

Author rebuttal:

Meta-review: The paper introduces an SE(3)-equivariant adapter framework for parameter-efficient fine-tuning of geometric diffusion models. Reviewers found the work well-motivated, well-written, technically sound, and supported by comprehensive experiments showing competitive performance. While concerns were raised about limited novelty and missing experimental details, these were mostly addressed during the rebuttal, leading to consistent acceptance recommendations. I therefore recommend accepting the paper.
Decision: Accept (poster)