GaussianFusion: Gaussian-Based Multi-Sensor Fusion for End-to-End Autonomous Driving
Authors: Shuai Liu
Quanmin Liang
Zefeng Li
Boyang Li
Kai Huang
Venue: NeurIPS 2025 spotlight ()
Keywords: End-to-End Autonomous Driving
Multi-Sensor Fusion
Gaussian
Primary area: applications

Abstract: Multi-sensor fusion is crucial for improving the performance and robustness of end-to-end autonomous driving systems. Existing methods predominantly adopt either attention-based flatten fusion or bird’s eye view fusion through geometric transformations. However, these approaches often suffer from limited interpretability or dense computational overhead. In this paper, we introduce GaussianFusion, a Gaussian-based multi-sensor fusion framework for end-to-end autonomous driving. Our method employs intuitive and compact Gaussian representations as intermediate carriers to aggregate information from diverse sensors. Specifically, we initialize a set of 2D Gaussians uniformly across the driving scene, where each Gaussian is parameterized by physical attributes and equipped with explicit and implicit features. These Gaussians are progressively refined by integrating multi-modal features. The explicit features capture rich semantic and spatial information about the traffic scene, while the implicit features provide complementary cues beneficial for trajectory planning. To fully exploit rich spatial and semantic information in Gaussians, we design a cascade planning head that iteratively refines trajectory predictions through interactions with Gaussians. Extensive experiments on the NAVSIM and Bench2Drive benchmarks demonstrate the effectiveness and robustness of the proposed GaussianFusion framework. The source code is included in the supplementary material and will be released publicly.

GaussianFusion: Gaussian-Based Multi-Sensor Fusion for End-to-End Autonomous Driving
Shuai Liu, Quanmin Liang, Zefeng Li, Boyang Li, Kai Huang School of Computer Science and Engineering, Sun Yat-sen University (liush376@ mail2, liby83@ @mail, muangk36@mail).syyu...
Abstract
Multi-sensor fusion is crucial for improving the performance and robustness of end-to-end autonomous driving systems. Existing methods predominantly adopt either attention-hain eeeeet flatten fusion bird's eye view fusion through geometric transformations. However, these approaches often suffer from limited interpretabil- ity dense computational overhead. In this paper, introduce Gaussian FusssinnFusion. a Gaussian-based multi-sensor fusion framework for end-to-end autonomous driving. Our method employs explicit and compact Gaussian representations intermediate carriers to aggregate information from diverse sensors. Specifically, we initialize set of 2D Gaussians uniformly across the driving scene, where each Gaussian is parameterized by physical attributes and equipped with explicit and implicit features. These Gaussians are progressively refined by integrating multi-modal features. The explicit features capture rich semantic and spatial infor- mation about the traffic scene, while the implicit features provide complementary cues beneficial for trajectory planning. To fully exploit rich spatial and semantic information in Gaussians, we design a cascade planning head that iteratively refines trajectory predictions through interactions with Gaussians. Extensive experiments on the NAVSIM and Bench2Drive benchmarks demonstrate the effectiveness and robustness of the proposed GaussianFusion framework. The source code is released at htttps://githu/ / com/ Soon/SayLL/// Saayy2//Guss Gaussissi iisssinFuus Fusion
Introduction
End-to-end (E2E) autonomous driving [6 25 4 32 has attracted growing attention for its potential to streamline the traditional modular pipeline by directly mapping sensor inputs to driving actions through deep learning. This paradigm reduces system complexity and enables joint optimization across tasks. However, relying on a single sensor often limits the system's 's ability to handle diverse and challenging driving scenarios. To address this limitation, multi-sensor fusion has become essential, as it allows the model to leverage complementary information from different sensors such cameras, LiDARs, and radars. This integration enhances perception reliability and provides richer input for learning robust driving policies.
Existing multi-modal fusion strategies in E2E autonomous driving can be broadly divided into two categories: flatten fusion and bird's eye view (BEV) fusion. Flatten fusion methods [7] 36]] M [S
typically compress sensor features, such as those from images and LiDAR point clouds, into shared latent space, where feature interaction is performed using attention mechanisms, as shown in Figure (a). These approaches are appealing due to their flexibility and efficiency, often requiring minimal geometric calibration. However, the lack of explicit spatial grounding in 3D space limits their interpretability and makes them less effective in scenarios requiring precise spatial reasoning. project multi-modal features into common BEV
In contrast, BEV fusion methods 22
35
30
45
Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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coordinate, leveraging geometric priors to align data from different sensors, shown in Figure (b). This facilitates structured spatial understanding and improves performance in downstream perception tasks such as 3D object detection and map construction. Nevertheless, BEV fusion incurs significant computational and memory overhead due to the dense nature of the BEV representation, especially when high-resolution inputs or fine-grained features are involved. As result, there remains an ongoing challenge to develop fusion frameworks that can balance spatial awareness, efficiency, and scalability in complex driving environments.
3D Gaussians have recently gained attention in camera- based 3D scene representation and re-
Ga) Flatten CaitenFFFeee Funsen Methorls
due to their physical interpretability, compactness, and inherent spar- sity. These properties make them promising can- didates for multi-sensor fusion in autonomous driving, where efficiency and structured spatial understanding are critical. However, applying Gaussian representations in this context intro- duces several challenges. First, it is difficult to effectively supervise Gaussian parameters due to the lack of fine- grained 3D scene annotations in existing E2E driving datasets
construction [26 18 17]
Flaten
Image Encoder
Multi
Attention
Fused Fiztton Pretume
Points Encoder
Points Plation Features
Prizt Closg HFV Fresen Methoos
Encoder
Transformation
23 [49]
Kult! V Viww Imaaee
OR +
Second, existing approaches [8 17 mainly fo-
Imagee BFV Teeruma
FuRoi BEV Featune
cus on 3D scene representation, leaving their suitability for the motion planning task under- explored. Third, efficiently leveraging Gaussian representation for accurate trajectory generation requires careful architecture design. Address- ing these issues is key enabling Gaussian- based representations in E2E autonomous driv- ing frameworks.
Paints Encoder
Concaterala Openaiion
Plas Ogendioo
Fistures
Point
6c Our Ganesian Fusson Methool
Image Encoder
Kulti View Images
Refinement
Refined Gaussizzs
Points Encoder
Points BEV Featurs
With the aforementioned innovations and con- siderations, propose GaussianFusion, Gaussian-based multi-sensor fusion framework for E2E autonomous driving. Our approach leverages 2D Gaussians to represent the traf- fie scene, offering improved efficiency over 3D Gaussians. Notably, 2D Gaussians require su- pervision only from BEV semantic maps, which are widely available in E2E datasets [|] To tailor the fusion process to the motion planning task, we design dual-branch fusion pipeline. The first branch captures local features from multi-sensor inputs for each Gaussian and is primarily responsible for traffic scene reconstruction. The second branch aggregates global planning cues from the same inputs and is dedicated exclusively to motion planning. Moreover, to fully exploit the representational capacity of Gaussians, we introduce cascade planning module that refines the anchor trajectories by querying the Gaussian representations in a cascaded manner.
Figure 1: Pipelines of different multi-sensor fu- sion methods.
We evaluate GaussianFusinn on the planning-oriented NAVSIM dataset [. Utilizing the V2- 99 backbone (27). our approach achieves 92.0 PDMS [.., significantly surpassing current state- of-the-art methods. To further evaluate the generalization and robustness of our framework, we conduct experiments on the closed-loop benchmark Bench2Drive (23), where the results consistently demonstrate the effectiveness of GaussianFusion. The key contributions of this work are summarized as follows:
We first introduce Gaussian representations into the domain of multi-sensor fusion for E2E autonomous driving, and we propose a dual-branch fusion pipeline tailored to the p planning-centric task.
We design a cascade planning head specifically adapted to the Gaussian representation, which iteratively refines trajectories through hierarchical Gaussian queries.
Extensive evaluations on both open-loop (NAVSIM) and closed-loop (Bench2Drive) bench- marks demonstrate the superior performance and robustness of GaussianFusion.

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2
Related Work
End-to-End Autonomous Driving. E2E autonomous driving approaches can be broadly categorized into single-task and multi-task methods. Single-task methods 3 8 9 primarily focus the planning task. An early work [3] employs a convolutional neural network (CNN) to directly map raw pixel data from front-facing camera to steering commands. Building on this idea, [ proposes conditional imitation learning, which extends traditional imitation learning by integrating high-level navigational commands to better capture driver intent. CILRS O|] further explores behavior cloning within the E2E framework, aiming to improve performance through more structured supervision.
Multi-task methods extend the E2E autonomous driving paradigm by incorporating auxiliary tasks such as 3D object detection, mapping. and motion forecasting. Compared to single-task approaches, the multi-task paradigm enables the learning of scene representations with improved generalization and interpretability [9]. This has led to growing interest from the research community. UniAD [16] introduces a planning-oriented framework that sequentially integrates perception, prediction, and planning modules. VAD (25) and its improved version VADv2 [4] adopt a vectorized scene representation enhance computational efficiency. More recently, diffusion- based strategies [6] have gained attention in E2E autonomous driving. GoalFlow 43 introduces goal-conditioned denoising, leveraging goal points guide the generation of multi-modal trajectories. DiffusionDrive (32 proposes a truncated diffusion policy to accelerate the denoising process, improving inference speed without sacrificing trajectory quality.
Sensor Fusion for Autonomous Driving. Existing sensor fusion approaches can be generally classified into flatten fusion and BEV fusion methods. Flatten fusion methods [36 7 20
typically compress image and LiDAR features into flattened representations, which are then fused
using attention mechanisms 33 40).
For example, InterFuser (36) concatenates flattened features
from multiple sensors and applies self-attention [39] to enable information exchange. TransFuser follows the same paradigm but incorporates multi-scale features enhance fusion. To mitigate the influence of irrelevant image regions, TransFusion [T] introduces a 2D circular Gaussian mask that modulates the cross-attention weights. AutoAlign (5) further improves upon this by introducing cross-attention-base feature alignment module that adaptively aggregates pixel-level image features for each voxel. While these methods eliminate the need for explicit calibration, they often suffer from limited interpretability and lack the capability for explicit 3D scene modeling.
7 20
30 45 typically fuse multi-modal features within the BEV plane based on geometric projection relationships. MILE [15] lifts image features into 3D using predicted depth distributions, then aggregates voxel features into BEV via grid-based sum-pooling. ContFuse 3i employs 3D point clouds as intermediaries to project pixel-level image features onto the BEV plane for fusion. ThinkTwice [22] and Adiperr [2] adopt the LSS framework (35) to transform image features into BEV space, which are then concatenated with R-dervdd BEV features. BEVFormer (30) and FusionAD [45) further extend the BEV representation by incorporating a height dimension into the BEV queries, enabling spatially-
BEV fusion methods 31
22
35
fcature extraction from image inputs. This type of method addresses the interpretability and 3D modeling limitations inherent in flatten fusion methods. However, since operating on a dense BEV grid, these methods often incur significant computational and memory overhead.
In contrast to existing fusion paradigms, we propose GaussianFusion, which leverages Gaussian representations as intermediaries to extract and aggregate mudti-modal features. Gaussians well- regarded for their strong scene reconstruction [26] and explicit representation properties. Moreover, Gaussian representations are sparsely distributed in space, in stark contrast the dense grids used in BEV fusion methods. As a result, our Gaussian effectively circumvents the limitations of both flatten fusion (lack of structure and interpretability) and BEV fusion (computational and memory inefficiency), offering a more efficient and interpretable alternative for multi-sensor integration.
Gaussian Representation. 3D Gaussian Splatting (3D-GS) (26] first introduced 3D Gaussians as scene representation for radiance field rendering, achieving high visual fidelity and real-time perfor- mance. Deformable-GS [44] extends this technique to dynamie scene reconstruction and rendering. Other works [38] 46 adapt Gaussian splatting for 3D content creation. The GaussianFormer series utilizes 3D Gaussians perform occupancy prediction.
18
17
The approach most closely related to ours GaussianAD 48 which models future scene evolution using Gaussian flows. While both methods leverage Gaussians for representing traffic scenes, our
3

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Gaussian Inillization Plysiiaal trributtes
Gaussian Encoder Block
Cross A Un.
Self Un.
Map
Implicit
Gaussion
Construction
Retize
Explicti Feallures
Deformable Atn.
Self Atn.
Semandcc
Jesillive
Map
Atchor
Cascade Planning
Trajectoriee
Piniiial Aftextion
Cinss Attertion
Quxy
Image& Points Encoder
Y Retined Trajectoctes
Image Features
Point BEV Festures
Explicto& Emplicit
Kev&Va
[terntivee
Multi- Senttrre Input
Features
Figure 2: The overall framework of our GaussianFusion Given raw multi-sensor data as input, GaussianFusion first extracts image and point features using a backbone network. It then initializes a of Gaussians, which iteratively refined through Gaussian encoder blocks. Finally, the refined Gaussians are used to construct the semantic map and to iteratively adjust the anchor trajectories.
GaussianFusion differs from GaussianAD in several key aspects: 1) GaussianFusion designed for multi-sensor fusion in E2E autonomous driving, whereas GaussianAD focuses solely on vision- based systems. 2) Our method employs 2D Gaussians as scene representations,
contrast to 3D Gaussians used in GaussianAD. This design choice enables supervision using only BEV-level annotations (e.g., semantic maps and agent states), eliminating the need for dense 3D occupancy labels and significantly improving computational efficiency. 3) Additionally, GaussianFusion incorporates dual-branch feature fusion design tailored for the planning-cene ceetinggcenntic task.
Method
The objective of E2E autonomous driving is predict the future trajectory of the ego vehicle directly from raw sensor inputs. Formally, given multi-view images I [I E TR x LiDAR points P R=x3 and transformation matrices T = (T; IR 3x3
I...., N). i= 1, NY. the goal is to predict the ego vehicle trajectory т {( yr ) where N, (H, W), (Iz, and T denotes the number of views, the image resolution, the number of points, the waypoint coordinate time and the planning horizon, respectively.
The overview of our GaussianFusson is illustrated in Figure It can be divided into three phases as follows: (1) Gaussian initialization (Sec. [.1]; (2) Gaussian encoder: Gaussians from multi-sensor
(Sec. 3.2 (3) Gaussian decoder: Gaussians to scene reasoning (Sec. 3.3
3.1
Gaussian Initialization
Given that autonomous vehicles primarily operate on planar surfaces, Gaussians suffice to model the traffic scene. Specifically, we randomly generate set of 2D Gaussians G [G; - 1,..., P). where P denotes the predefined number of Gaussians. Each Gaussian characterized by both physical attributes and hidden features. The physical attributes include mean IR3 scale R² rotation r e I2, and semantic logits с e RC, where C' is the number of semantic categories. The rotation is represented using its sine and cosine components. The hidden features consist of both explicit and implicit features, which are then refined through two separate branches. Further details regarding the explicit and implicit features are provided in Sec. 3.2
3.2 Gaussian Encoder: Gaussians from Multi-Sensor Fusion
To learn meaningful Gaussian representations, we first utilize two independent backbones to extract multi-scale features from images and LiDAR points. These features are then used to iteratively

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refine both the physical attributes and hidden features of Gaussians. Each iteration consists of point cross-attention module, an image cross-attention module, Gaussian self-attention module, and refinement module. The hidden features of each Gaussian are divided into explicit and implicit components, each serving distinct roles. Explicit features are derived from local regions of multi- sensor inputs via explicit geometric transformations and are responsible for updating the physical properties of Gaussians. In contrast, implicit features interact with global multi-sensor features without relying geometric transformations, and are used exclusively for trajectory planning.
Point Cross-Attentions to extract information from point features. Specifically, for each Gaussian G = {m, s, C, fexp, f"mP) } (z,, 34)
Gaussians from Points. point aotssatttntion (PCA) module is employed
we generate a set of query points of the i-th query point, and n is the total number of queries. Following [18]. the query set includes both fixed and learnable points: the fixed queries are distributed around each Gaussian based on its covariance matrix, while the learnable queries are constrained within the interior of the Gaussian. Given multi-scale point feature maps M (M² E dd Hf. x xWT
I,..., ng). where (zg, y4 denotes the location
1, ,,...,,,),, where (H,, W?) denotes the resolution of the i-th scale feature map and n, the number of scales, we apply deformable attention layer 42 to aggregate information from these features and update the explicit features of Gaussians.
R4
peopi
DeAttn (F 2)),
where grapp denotes the updated explicit features using multi-scale point features, Q indicates the i-th point in Q, and (eAttan-) represents the deformable attention. For the implicit features, we use a vanilla cross-attention 44 to build interactions with the last scale point features F.
pimpt = -CrssAAtn (Pimp, MY.)).
(2)
where gimpt denotes the updated implicit features, and CrossAttn refers to the cross-attention layer. For brevity, we omit the residual connection and ferd-forward network (FFN) components in the formulation. The resulting updated Gaussian is represented as G {m, r. foxpí, rimpt). Note that, for clarity, we illustrate the process using single Gaussian as an example.
Gaussians from Images. To incorporate visual information from multi- view images, we employ an Image Cross-Attention (ICA) module. Similar the PCA module, ICA generates both fixed and learnable query points for each Gaussian. However, these queries additionally incorporate height information to enable projection into the image plane. Specifically, we first generate 2D query points Q2a = {22, y:) i= I..... ..y. identical to those used in the PCA module. For each 2D query location, we then uniformly sample np pillar points along the vertical axis. The bottom of each pillar is fixed at 2 mmin. while the top is parameterized by learnable variable 2g E [zmin: 2max]) where 2min and 2max define the vertical bounds of the traffic scene. This results in set of 3D query points Qad {x,,, U/. 2;) i= 1, .............................. .Ry x mpp) Given the I,..., n,) extracted by the image backbone, where (H! W denote the resolution of the i-th scale feature map and N the number of camera views, the explicit and implicit features of Gaussians are computed as follows:
Image
multi-scale image feature maps M = (M/ E RdxNxH( xW;
12 X
pezpt
DeAutn (pezpt, Cas [1] M²), pimpt CrossAttn (pimpt M
where Qaa[i] denotes the i-th 3D query point in Qsd. Following the PCA module, we obtain the updated Gaussian representation G [m, s.r. c, foxpt fimpt).
Gaussians Refinement Module. After aggregating information from multi-modal features, we further refine the Gaussian representations. Specifically, we employ two separate self-artention layers [39] to build interactions among all Gaussians-one for the explicit features and the other for the implicit features:
5

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{f
SelfAttn pp pappy fel (e,
pimpr
phmpt
SelfAttn((f) (pimpt Ip mp)),
plmpl (pl......p))..
(4)
(el,.... ep
PosEmbed((mm)
where e denotes the positional embedding of the i-th Gaussian, SelfAtten(-) and (osEmbed()) refer to the self-attention and positional embedding layers [33,, respectively. Subsequently, following
[8]. a multi-layer perceptron (MLP) is employed to refine the physical attributes Gaussians based on their explicit features:
G' = (m' m,s',', r c', geepp ffmm") (m','',r'','' MM
(5)
The Gaussian encoder deseribed above is applied iteratively refine the Gaussian representations. The final updated Gaussians are then passed to the Gaussian decoder, which performs downstream tasks such mapping and planning.
3.3 Gaussian Decoder: Gaussians to Scene Reasoning
To effectively regulate the 2D Gaussians, we design Gaussian decoder comprising two components: map construction and cascade planning. The map construction module explicitly reconstructs the traffic scene, providing backpropagation gradients that guide the Gaussian encoder in refining the physical attributes and explicit features. Following [17]. we implement this module using probabilistic Gaussian superposition; further details are provided in Appendix A The cascade planning module generates trajectory predictions in a cascaded manner, where each subsequent output is refined based on the preceding one. addition to leveraging the explicit features, it also incorporates the implicit features obtained from the Gaussian implicit fusion branch.
28 which constructs an anchor trajectory vocabulary based on the trajectory distribution observed in the dataset. Given the set of Gaussians obtained from the Gaussian encoder, we refine anchor trajectories A {A, I,..., k) in cascaded manner, where 7 denotes the planning horizon and the number
Cascade Planning. We adopt an anchor- anchor-based planning strategy
RTx2 X2 of trajectory points. Taking a single anchor trajectory distance between each of its trajectory points and all Gaussians. For each point, we select its top-m nearest Gaussians, forming a Gaussian subset Я = (G, (....,..,,m7 The anchor feature F A then obtained by querying this Gaussian set:
E A as an example, we first compute the
FA CrossAtta(F query: Fg2),
F query = Embedding( (A),
(6)
FçA- (( pimp) 1;:.,...,m
where CrossAttn denotes cross-attention layer, and Embedding represents an embedding layer that encodes the anchor trajectory A into initial query feature F query. The terms f. and r.t refer to the explicit and implicit features of the Gaussian G; E GA. respectively, and [rexp r.mP)] denotes their concatenation. The traffic map and surrounding agents be decoded from the most recent Gaussians G, enabling & to serve as comprehensive representation of the traffic scene. Therefore, we employ cross-attention layer build interactions between the anchor feature F A and hidden features of G. The refined trajectory { yt) bt) is obtained as follows:
MLP((F.) .) + A. F Cross FA Fg).
F [
f. pimp
| I..
The trajectory is refined in cascaded manner, where the output trajectory 7 from the current stage used as the anchor input for the subsequent stage, iteratively repeating the steps described in End Eq. (referred to as Gaussian Spatial Attention and Gaussian Cross Attention in Figure 2 respectively). We adopt the same trajectory loss function as proposed in to supervise the cascade refinement process.

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Method
Input
Img. Backbone
NC
DAC1
TTC 1
EP
PDMS
LTF
C
ResNet34
97.4
92.8
92.4
79.0
83.8
TransFuser
C I.
ResNet34
97.7
92.8
93.0
79.2
84.0
GoalFlow
C& L
ResNet34
98.3
93.3
94.8
79.8
85.7
Hydra-MDP
C I.
ResNet34
98.3
96.0
94.6
78.7
86.5
Hydra-MDP++
C
ResNet33
97.6
96.0
93.1
80.4
86.6
ARTEMIS
C & I.
ResNet34
98.3
95.1
94.3
81.4
87.0
DiffusionDrive
C & L
ResNet34
98.2
96.2
94.7
82.2
88.1
GaussianFusion (Ours)
C & I.
ResNe(34
98.3
97.2
94.6
83.0
88.8
GoalFlow
C & I.
V2-99
98.4
98.3
94.6
85.0
90.3
Hydra-MDP-C
C
V2-99
98.7
98.2
95.0
86.5
91.0
Hydra-MDP++
C
V2-99
98.6
98.6
95.1
85.7
91.0
GaussianFusion (Ours)
C L
V2-99
98.7
98.1
95.7
88.2
92.0
Table I: Performance on the Navtest Benchmark with Original Metries. 'C' and 'L' represent
camera and LiDAR modality, respectively. Definitions of sub-metries are provided in Appendix The best results of different backbones are highlighted in bold, separately.
Method
NC 1
DAC
EP
TTC
DDC 1
LK
EC f
EPDMS
TransFuser'
7
97.7
92.8
79.2
92.8
98.3
67.6
95.3
77.8
VADv2"
97.3
91.7
77.6
92.7
98.2
66.0
97.4
76.6
Hydra-MDP
29
97.5
96.3
80.1
93.0
98.3
65.5
97.4
79.8
Hydra-MDP+4
28
97.9
96.5
79.2
93.4
98.9
67.2
97.7
80.6
ARTEMIS
98.3
95.1
81.5
97.4
98.6
96.5
98.3
83.1
DiffusionDrive
32
98.2
96.2
87.6
97.3
98.6
97.0
98.4
84.0
GaussianFusion (Ours)
98.3
97.3
87.5
97.4
99.0
97.4
98.3
85.0
Table 2:
Performance on the NAVSIM navtest split with extended metries. represents that the The best results are highlighted in bold.
results are sourced from Hydra-MDP+4 (28)
4 Experiments
4.1 Benchmark and Metric
We evaluate models on NAVSIM and Bench2Drive 23 benchmarks. NAVSIM, built upon the OpenScene dataset [0]. provides 120 hours of challenging driving data with high-resolution camera images and LiDAR inputs spanning up to 1.5 seconds. It filters out trivial driving scenarios to emphasize complex mecision-making. We use the official Predictive Driver Model Score (PDMS) and its extended version, EPDMS (28) as evaluation metrics. Bench2Drive
2 based on the CARLA
simulator [2], evaluates E2E autonomous driving across 220 routes that cover interactive scenarios under diverse conditions. We adopt the CARLA Driving Score (DS) and multi-ability metrics for fine-grained assessment. For more details about these metrics, please refer to Appendix
4.2 Implementation Details
For the NAVSIM benchmark, left-front, and right-front cameras, along with LiDAR point clouds. The camera images are cropped to resolution of 448 250. For the Bench2Drive (23 benchmark, we adopt only the front-view camera, which already provides a wide field of view. In this case, we use the resolution of 1024 x 384, which consistent with the setting used in TransFuser++ [4)]. For the benchmarks, LiDAR points projected onto the BEV plane, following the approach in TransFuser (7]. In our main experiments, 512, and each Gaussian feature has a dimensionality of 128. We
the NAVSIM train split for training. We utilize input from front,
the number of Gaussians is adopt 4 GaussianEncoder blocks and 2 cascade planning blocks. The number of anchor trajectories is set to following 332 is worth noting that map construction module
Geussia is detached during inference for efficiency. Training is performed using the AdamW optimizer [34]. with 50 epochs, weight decay of x 10-4, and maximum learning rate 10-1, which follows analysis is in Appendix
cosine annealing schedule for learning rate decay.

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Overallt
Multi-Ability EBrake
Method
SR
Merge
Overtake
GiveWay
TSign
Mean
PDM-Lite
97.0
92.3
88.8
93.3
98.3
90.0
93.7
92.8
AD-MLP
0.0
0.0
0.0
0.0
0.9
TCP [1
40.7
15.0
16.2
20.0
20.0
10.0
7.0
14.6
VAD
255
42.4
15.0
8.1
24.4
18.6
20.0
19.2
18.1
UniAD
16
16.4
17.8
21.7
10.0
15.6
ThinkTwice
62.4
33.2
35.8
50.0
37.2
DrivcTransformer
2
63.5
35.0
17.6
35.0
48.4
40.0
52.1
38.6
DriveAdapter
64.2
33.1
28.8
26.4
48.8
50.0
56.4
42.1
TF++
49
76.9+-0.9
54.0+110
48.8+
37.6+7.0
64.2++8.4
50.0+0.0
59.7++6.1
52.0=3.0
GaussianFusion (Ours)
79.1=1111
54.4#2.6
36.6:3.3
64.4
66.5#6.4
53.3+:.88
60.8
56.3=3.7
Table Performance on the Bench2Drive benchmark. 'SR', 'EBrake', and "TSign' denote the success rate, emergency braking, and traffic sign compliance, respectively. PDM-Lite is a rule- based planner that can access privileged information from the CARLA simulator. *** denotes the implementation of the same backbone and training dataset setting as our method.
Gaussian Exp. Fusion
Gaussian Imp. Fusion
Cascade Planning
Agent Pred.
Param.
DAC
TTC1
EP
LKt
EPDMS
X
55.7M
94.1
96.9
87.5
96.2
81.8
x
49.6M
96.5
97.1
87.8
97.0
84.2
X
x
51.6M
96.6
97.3
87.8
97.3
84.5
X
X
53.7M
97.0
97.2
87.4
97.2
84.4
X
55.8M
97.3
97.4
87.5
97.4
85.0
V
59.5M
96.2
97.3
87.6
97.0
83.8
Table Ablation study of different architecture configurations. We utilize TransFuser the agent prediction head as the baseline model (the first row setting).
without
4.3 Comparison with State-of-the-Art Methods
Results on NAVSIM. We benchmark GaussianFusion against leading state-of-the-arr (SOTA) meth- ods on the NAVSIM navtest split. We employ ResNet34 [14 and V2-99 [27 as the image backbone of GaussianFusion respectively. As shown in Table our method significantly surpasses previous meth- ods, particularly on critical sub-metrics like DAC and Ego Vehicle Progress (EP) under the ResNet34 setting. Our enhanced GaussianFusion equipped with V2-99, further improves performance across all metrics-achieving state-of-the thette-rrt results on the Navtest benchmark. This demonstrates the scalability of our framework with stronger backbones. Additionally, the EPDMS metric. Note that EPDMS poses stricter challenge than PDMS by incorporating more nuanced driving criteria. As shown in Table 2 approach achieves 85.0 EPDMS, outperforming recent strong baselines such as 32 and 13 by 1.0 and 1.9 points, respectively. closer look reveals that most gains come from the Drivable Area Compliance (DAC) and Lane Keeping (LK) sub-metrics, indicating that GaussianFusion enables more stable and context-aware behavior in complex environments. These results consistently affirm the robustness and effectiveness of method across multiple evaluation protocols.
evaluate performance under
Results on Bench2Drive. We further conduct experiments the closed-loop benchmark, Bench2Drive, to compare our method with existing SOTA E2E methods. Due to high perfor- mance variability in the CARLA simulator, report results across three different random seeds. As shown in Table 3 our method, GaussianFusion, achieves the best overall performance (79.4 DS), outperforming all learning-basee based baselines. It shows balanced strength across diverse tasks, with notable gains in overtaking and traffic sign compliance. Compared to the rule-based privileged method PDM-Lite, method still falls short to extent, indicating that there remains substantial room for improvement in E2E autonomous driving methods.
4.4 Ablation Study
Effect of Different Components. To understand the impact of each design choice in GaussianFusion. we perform controlled ablation study by incrementally adding Gaussian Explicit Fusion (Gaussian Exp. Fusion), Gaussian Implicit Fusion (Gaussian Imp. Fusion), the Cascade Planning head

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Figure 3: Visualization of Gaussians during the refinement process. Gaussians with different semantics are shown in different colors.
Figure 4: Visualization of predicted and ground-truth trajectories, shown in red and green, respectively.
(Cascade Planning), and the Agent Prediction head (Agent Pred.) to the TransFuser baseline 77]. The results are shown in Table 4 Introducing Gaussian Exp. Fusion leads to a substantial +2.4 gain in EPDMS, while also reducing the parameter count. Adding Gaussian Imp. Fusion further improves performance to 84.5 EPDMS, with only a slight increase in parameters. Separately, incorporating Cascade Planning with only the explicit fusion also improves trajectory prediction, increasing LK and EPDMS compared to using explicit fusion alone. The best overall performance achieved when combining dual-branch fusion and Cascade Planning, reaching an EPDMS of 85.0. These findings confirm that our architectural components offer strong performance gains without significantly increasing model complexity. Finally, we observe that incorporating the agent prediction head degrades performance. We attribute this to the agent prediction task failing to provide effective guidance for the Gaussian refinement process, instead introducing ambiguity-wiir wwhat we refer to as Gaussian confusion. Given that the semantic map already encodes sufficient agent-related information, we remove the agent prediction head from our final design.
Different Multi-Sensor Fusion Methods. Table presents a comprehensive comparison of various multi-sensor fusion methods in terms of model parameters, semantic map construction, trajectory planning, and inference latency. The latency is measured by an RTX3090, To ensure a fair comparison, all methods adopt the same backbone and task heads.
Compared with the BEV fusion method, our Gaussian fusion achieves better performance (+0.04 mloU and +0.7 EPDMS), while also significantly reducing computational cost: the FLOPs are 38.9% lower and latency reduced by 25.6%, showing clear advantages in both accuracy and efficiency. Compared with the flatten (TransFuser-stylee) fusion, which is a very lightweight approach, our method exhibits only 30.3% increase in FLOPs, while achieving much stronger perfor- mance (+0.05 mIoU and +2.7 EPDMS). How- ever, our method's latency is 77.8% higher, which we believe is largely due the differences in operator-level optimization. This could be further mitigated through engineering improve-
Fusion Method
Latency! (ms)
Param.
FLOPs (G)
mioU!
EPDMS
Flatten BEV
27.4
51.9M
58.4
0.51
83.8
43
Gaussian
51.6M
35.7
0.55
84.5
Table 5: Comparison of fusion methods.
ments in deployment.
4.5
Qualitative Comparison
To provide an intuitive understanding of the refinement process in the Gaussian encoder, we visualize the spatial distribution of Gaussians at different refinement stages, as shown in Figure At the initial stage, Gaussians are evenly dispersed throughout the scene, As refinement proceeds, they progressively converge toward foreground regions. This behavior highlights the advantages of the Gaussian representation, which offers more compact and adaptable alternative to traditional dense BEV maps. More visualizations of Gaussians shown in Figure in the Appendix. We also present

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predicted ego-vehicle trajectories under variety of traffic scenarios in Figure 4 To qualitatively evaluate the prediction accuracy, we compare these trajectories against ground-truth data. In the leftmost scenario of Figure the vehicle makes an unprotected left turn without signal guidance- challenging case. Our method still predicts a trajectory closely matching the ground truth. addition, as shown in the two rightmost scenarios of Figure 4 our method is capable of producing accurate trajectory plans even in dense traffic conditions, further demonstrating its robustness and reliability.
Conclusion
In this work, we propose GaussianFusion, a Gaussian-based multi-sensor fusion framework for E2E autonomous driving. By utilizing compact and flexible 2D Gaussian representations, our method balances spatial awareness with computational efficiency. A dual-branch fusion architecture captures both local details and global planning cues from multi-modal inputs, while cascade planning module progressively refines trajectory predictions. Experiments on NAVSIM and Bench2Drive benchmarks show that GaussianFusion significantly improves planning performance with high efficiency. These results underscore the promise of Gaussian representations for efficient and interpretable sensor fusion in the E2E autonomous driving system. The limitation of Gaussian Fusion lies its customized CUDA operations, which are not fully optimized. In future work, we plan to either further optimize these operations or replace them with operations of a well-established neural network library.
Limitations. We have not conducted quantitative evaluations on tracking small or mostin objects. Similarly, our method has been assessed under sensor occlusion or noise, which critical factors for real-world deployment. Moreover, our method depends on 3D bounding box and road topology labels to optimize the 2D Gaussians. While effective, such supervision can be expensive or unavailable in real-world scenarios.
Acknowledgments
This work supported in part by the the Guangxi Key R & D Program under Grant No.Guike G...keeB240110224, and in part by the Guangdong Basic and Applied Basic Research Foundation under Grant 2025A151501 1485.
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(b)
(d)
Figure 5: Visualization of Gaussians of different inputs during the refinement process. Gaussians with different semantics are shown in different colors.
A Map Construction
Following [17], we utilize Gaussian probability superposition to construct the semantic map. Specif- ically, for map pixel position x E IR?, we first calculate its probability of falling different Gaussians:
a(x; G.) = exp (- 1
(-2 m;) m;)"Tx+(x m:)
(8)
Σ, = RSS = diag(s).)) (s.), R r2m((;)),
where m,, 8,, and r; denote the mean, scale, and rotation vectors of the Gaussian G,, respectively. Σ, represents the covariance matrix G;; diag(-) denotes the operator that constructs diagonal matrix from given vector; and r2m(-) denotes the function that converts rotation vector into its corresponding rotation matrix. Then the superposition probability can be calculated as:
DE (x G.) E..
((x:9)= =
Σ ( x) cj
Σ ( Gj) aj
(9)
(x G.)
exp
(x (x m)
"x (x m)
2mm))
where (x; G.) denotes the logits of different semanties on x, a; represents the prior probability of the existence of i-th Gaussian which is predicted by the network, and p(G, x) indicates the
14

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Encoder Blocks
Gaussian Numbers
DACT
TTC1
EPT
LK1
EPDMST
DAC
TTC1
EPT
LK
EPDMS
97.1
97.5
87.4
97.5
84.6
96.6
97.3
87.6
97.1
84.1
97.3
97.4
87.5
97.4
85.0
512
97.3
97.4
87.5
97.4
85.0
97.1
87.7
97.2
84.7
768
97.2
97.5
87.4
97.5
84.8
Table 7: Effect of the number of encoder blocks.
Table Impact of the number of Gaussians.
posterior probability the i-th Gaussian being present given the observation at x. Based on these quantities, can derive the probabilities for the background and foreground:
P
(x(x) = II (1 (xx G:)) E R
(10)
==1
pr(x) = (1 (x()) Softmax(o(x;;))) 9)) E R.
where Pb( (x) and px()) denote the background and foreground probabilities of pixel Softmax represents the Softmax function. Intuitively, for background pixel Xb. the (xb) will decrease with Gaussians gather on X because pt, S (1 - (xE; G:)) holds for any Gaussian. Conversely, for foreground pixel xf. the (r(x:) will increase with Gaussians gather on due to - (xr) > (xx; G,) holds for any Gaussian. Therefore, Eq. will encourage Gaussians move foreground pixels, as demonstrated in Figure 3 Given background and foreground predictions [pt: pr] E RC+1
and ground-tre -tuth bev map, we employ cross entropy loss Lee and the lovasz-softmax loss Liov as
the map construction loss functions.
B Metrics
For the NAVSIM 11| benchmark, we adopt the
official Predictive Driver Model Score (PDMS)
Cascade Stages
and its extended version, Extended PDMS [28 (EPDMS), These metrics are designed to bridge the gap between open-loop planning bench- marks and closed-loop simulation evaluations. PDMS comprises multiple sub-metrics, includ- ing No-Collision (NC), Drivable Area Compli- ance (DAC), Time-to-Collision (TTC), Comfort (C), and Ego Vehicle Progress (EP), EPDMS extends this framework by incorporating additional criteria: Lane Keeping (LK), Extended Comfort (EC), Driving Direction Compliance (DDC), Traffic Light Compliance (TLC), and
DACT
TTC*
EPt
LKt
EPDMS
96.6
97.4
87.4
97.1
84.3
97.3
97.4
87.5
97.4
85.0
97.0
97.4
87.8
97.3
84.7
Table 8: Results of the stage of cascade planning.
Penalty Filtering, thereby offering a comprehensive
assessment of driving behavior.
For the Bench2Drive 23 benchmark, we employ the CARLA Driving Score (DS), which jointly considers route completion and penalties for traffic infractions. addition to DS, we also use multi-ability metrics that target specific driving skills of the autonomous driving system, such as merging, overtaking, yielding, traffic sign compliance, and emergency braking.
C Hyper-Parameter Analysis
In this section, we determine the optimal value for the number of Gaussians, the number of encoder blocks, and the stage number of cascade planning through experiments on the NAVSIM dataset. Table the impact of the number of Gaussians. When increasing the number of Gaussians from 256 to 512, the performance improved significantly. However, further enlarging the number of Gaussians does not bring gains. Table presents the effect of the number of Gaussian encoder blocks. Setting the number of encoder blocks to is the best choice. Since we only supervise the output of the last encoder block, too deep may affect performance. Table @ible@iiluaee illustrates the performance of different stage number of cascade planning. We observe that 2 cascade stages are enough to generate accurate trajectories.
15

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(a)
(b)
(c)
Figure 6: Failure mode of GaussianFusion in some scenarios.
D
Failure Mode
To better understand the limitations Gaussian in complex real-world scenarios, we visu- alize typical failure cases in Figure These cases reveal distinct behavioral biases in the learned policy, reflecting the implicit priors encoded in the training dataset and the conservative nature of GaussianFusion.
In Figure aa), the model demonstrates overly conservative behavior when executing turning ma- neuvers intersections. Compared with human experts who perform smooth and anticipatory turns, GaussianFusion tends to delay or narrow the turning trajectory. We hypothesize that this attributed to the data distribution, where the majority of demonstrated driving behaviors follow cautious and robust strategies, leading the model to learn a risk-averse policy in ambiguous topological regions.
Figure b) illustrates model behavior under adverse weather conditions such fog. In low- visibility scenarios, the model prioritizes stability by choosing slow and straight driving strategy rather than making proactive turning decisions. This behavior suggests that Gaussian primitives lose discriminative power degraded sensor conditions, causing the planner to rely on the safest longitudinal control instead of predictive planning.
Figure (cc)
reflects the model's tendency to maintain its lane and follow leading vehicle that is changing lanes, instead of performing an overtaking maneuver. This indicates a bias toward conser- vative following behavior in highly dynamic multi-agent scenarios. The model may underestimate the feasibility or safety margin of overtaking due to uncertainty in surrounding vehicle intentions, resulting reactive rather than assertive driving strategy.
Overall, these failure cases highlight that GaussianFusion inherits conservative driving priors from the dataset and tends favor low-risk behaviors when facing uncertainty. While such conser- vatism improves safety in most situations, it may limit driving efficiency or adaptability in complex environments.
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Reviews:
[{"review_id": "KBQQhEaz6W", "reviewer": "Reviewer_v3h9", "summary": "The paper presents GaussianFusion, a multi-sensor fusion framework for end-to-end autonomous driving. It uses learnable 2D Gaussian primitives to represent the driving scene, enabling efficient, interpretable fusion of camera and LiDAR inputs. The architecture separates scene understanding and planning via a dual-branch design and refines trajectories using a cascade planning head. Results on NAVSIM and Bench2Drive show improved planning performance over existing methods.", "questions": "* _Q1:_ How does or would the GaussianFusion perform under real-world challenges such as fog, occlusions, or sensor noise? Any plans to test beyond simulation?\n* _Q2:_ Do sparse Gaussians compromise resolution or miss small/fast-moving objects compared to BEV grids?\n* _Q3:_ Does the use of sparse 2D Gaussians lead to reduced spatial resolution or difficulty in capturing small (e.g., dog on a leash, little kids) or fast-moving objects compared to dense BEV-based representations?\n* _Q4:_ Do the implicit and explicit branches ever conflict or interfere? How is their interaction managed during training?", "limitations": "**Partially yes**. There is no dedicated Limitation section, just one sentence in the Conclusion where the authors mention the use of custom CUDA operations and acknowledge that performance may not be optimal. It would be great if authors include more points about, for example, (i) robustness to sensor failure, weather, or domain shift, (ii) generalization of 2D Gaussians (vs. 3D or hybrid methods), and (iii) failure cases.", "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- **STRUCTURE and LANGUAGE**: The paper follows a standard structure, which makes it easier to follow and read. Overall, the paper is well-written. The level of English is great. Figures are of good quality and improves the clarity. Formally, everything is on a high level.\n\n- **STRONG REPRODUCIBILITY**: The reproducibility is way above the standard. The code is provided, and implementation details (e.g., backbone, fusion modules, training settings, and hyperparameters) are clear.\n\n- **METHOD DESIGN**: The proposed methodology/architecture is well-motivated. Separating explicit spatial grounding (for map reconstruction) and implicit latent reasoning (for planning) is a clean and understandable. The use of 2D Gaussians seems like a good balance between efficiency and interpretability. The cascade planning head is well-integrated and shows clear performance gains.\n\n- **EMPIRICAL VALIDATION**: Experiments are thorough and wide. Authors evaluate both open-loop (NAVSIM) and closed-loop (Bench2Drive) performance. Ablations support each component’s contribution. The method achieves state-of-the-art or very competitive performance in several key planning metrics with fewer parameters.\n\n- **QUALITATIVE ANALYSIS**: Visualizations of the Gaussian refinement process and trajectory outputs offer intuitive insight into the model's \"performance\" and potential interpretability. The supplemented video is a cherry on top.\n\n\n### **Weaknesses**\n- **INCREMENTAL NOVELTY**: Although the framework is well thought out / developed, the core ideas (Gaussian scene representations, dual-branch pipelines, cascade planning) build upon existing methods (e.g., GaussianFormer, TransFuser, GaussianAD). The novelty lies in how these components are combined for E2E planning, not in any fundamentally new technique.\n\n- **LIMITED STATISTICAL RIGOR**: Like many NeurIPS submissions, the evaluation is based on single-seed results without any variance estimates, error bars, or confidence intervals (acknowledged by the authors). This is particularly important, given that some of the reported improvements over prior work (e.g., DiffusionDrive or ARTEMIS) are relatively small and could plausibly be attributed to randomness. Without repeated runs or statistical testing, it is difficult to assess whether the performance gains are robust or cherry-picked. \n\n- **SPARSE REPRESENTATION TRADE-OFFS**: While the use of sparse Gaussians improves computational efficiency, it is unclear how well this representation captures fine spatial details. Particularly in edge cases involving small or fast-moving objects, which is a major concern in end-to-end autonomous driving, where robustness to OOD objects (as emphasized in the COOOL benchmark [1, 2, 3]) is essential. Authors do not evaluate or discuss how well GaussianFusion handles such scenarios, nor compare it against denser representations.\n\n**[Additional Comments]:**\n- _Table and figure captions lack clarity:_ Table and Figure captions should be self-explanatory, i.e., understandable without needing to refer to the text. For Example, it is not clear what the colors and or the numbers in Figure 3 and Figure 5 represent.\n- _About Interpretability_: The claim that GaussianFusion is more interpretable is kind of intuitive, but no formal interpretability analysis (e.g., user study, attribution) is provided but could be beneficial for the contribution framing.\n- _Inconsistent bolding in figure captions_: The authors should standardize the use of bold text in figure / table captions. The inconsistance is not viaually apealing.\n- _Incorrect citation formatting_: The in-text referencing style does not follow NeurIPS guidelines. References should be (i) ordered numerically, i.e., not [8, 3, 5] but [3, 5, 8] and (ii) separated by commas (e.g., “[3, 5, 8]”), not semicolons.\n\n______\n\n[1] @article{alshami2024coool,\n  title={Coool: Challenge of out-of-label a novel benchmark for autonomous driving},\n  author={AlShami, Ali K and Kalita, Ananya and Rabinowitz, Ryan and Lam, Khang and Bezbarua, Rishabh and Boult, Terrance and Kalita, Jugal},\n  journal={arXiv preprint arXiv:2412.05462},\n  year={2024}\n}\n\n[2] @inproceedings{picek2025zero,\n  title={Zero-shot hazard identification in Autonomous Driving: A Case Study on the COOOL Benchmark},\n  author={Picek, Lukas and Cermak, Vojtech and Hanzl, Marek},\n  booktitle={Proceedings of the Winter Conference on Applications of Computer Vision},\n  pages={654--663},\n  year={2025}\n}\n\n[3] @article{shriram2025towards,\n  title={Towards a multi-agent vision-language system for zero-shot novel hazardous object detection for autonomous driving safety},\n  author={Shriram, Shashank and Perisetla, Srinivasa and Keskar, Aryan and Krishnaswamy, Harsha and Bossen, Tonko Emil Westerhof and M{\\o}gelmose, Andreas and Greer, Ross},\n  journal={arXiv preprint arXiv:2504.13399},\n  year={2025}\n}", "was_revised": true, "final_justification": "The authors have addressed my main concerns with a clear response and new results, including multi-seed experiments and further clarification of the sparse Gaussian representation. Their answers improve the paper’s clarity, especially regarding statistical reporting and empirical robustness. While some suggestions, such as real-world evaluation and formal interpretability analysis, remain as future work, these do not significantly affect my assessment of the technical quality or contribution. Reading other reviewers’ comments did not change my view. I will maintain my overall positive rating.", "rebuttal": ">**Q1. Although the framework is well thought out / developed, the core ideas build upon existing methods.**\n\nWe sincerely appreciate the reviewer's recognition of our overall framework design. Our approach is inspired by prior great works, including 3D Gaussian Splatting [1] and GaussianFormer [2]. Our key contribution lies in introducing **2D Gaussian scene representations** as a unified bridge for multi-sensor feature fusion in end-to-end planning. Notably, we are the first (to our knowledge) to apply 2D Gaussians for driving scene representation—a design that simultaneously achieves three critical advantages:\n\n1. **Flexible**: Positions and shapes of 2D Gaussians can be dynamically adjusted during the feed-forward process.\n2. **Efficient**: A few hundred 2D Gaussians are sufficient to model an entire driving scene.\n3. **Intuitive**: 2D Gaussians can be directly visualized during the refinement process.\n\nWe believe this design provides a different and practical perspective for scene representation in autonomous driving.\n\n>**Q2. The evaluation is based on single-seed results without any variance estimates, error bars, or confidence intervals.**\n\nThank you for your valuable comment. Following your suggestion, we conducted multi-seed experiments (three times) on both the NAVSIM and Bench2Drive benchmarks. As shown in the tables below, we report the mean and standard deviation.\n\n**Table 1. Performance on the Navtest Benchmark.**\n| Method               | Input | NC ↑ | DAC ↑ | TTC ↑ | EP ↑ | PDMS ↑ |\n|----------------------|-------|------|-------|-------|------|--------|\n| LTF               | Camera | 97.4 | 92.8  | 92.4  | 79.0 | 83.8   |\n| TransFuser        | C & L | 97.7 | 92.8  | 93.0  | 79.2 | 84.0   |\n| GoalFlow         | C & L | 98.3 | 93.3  | **94.8**  | 79.8 | 85.7   |\n| Hydra-MDP++       | C & L | 98.3 | 96.0  | 94.6  | 78.7 | 86.5   |\n| ARTEMIS           | C & L | 98.3 | 95.1  | 94.3  | 81.4 | 87.0   |\n| DiffusionDrive    | C & L | 98.2 | 96.2  | 94.7  | 82.2 | 88.1   |\n| GaussianFusion (Ours)| C & L | **98.4**±0.1 | **97.3**±0.1 | 94.6±0.2 | **83.1**±0.1 | **88.9**±0.1   |\n\n**Table 2. Performance on the Bench2Drive benchmark.** '*' denotes the results are reproduced by ourselves.\n| Method                     | DS  | SR  | Merge | Overtake | EBrake | GiveWay | TSign | Mean  |\n|----------------------------|-----|-----|-------|----------|--------|---------|-------|--------|\n| PDM-Lite                | 97.0| 92.3| 88.8  | 93.3     | 98.3   | 90.0    | 93.7  | 92.8   |\n| AD-MLP                  | 18.1| 0.0 | 0.0   | 0.0      | 0.0    | 0.0     | 4.4   | 0.9    |\n| TCP                     | 40.7| 15.0| 16.2  | 20.0     | 20.0   | 10.0    | 7.0   | 14.6   |\n| VAD                     | 42.4| 15.0| 8.1   | 24.4     | 18.6   | 20.0    | 19.2  | 18.1   |\n| UniAD                   | 45.8| 16.4| 14.1  | 17.8     | 21.7   | 10.0    | 14.2  | 15.6   |\n| ThinkTwice              | 62.4| 33.2| 27.4  | 18.4     | 35.8   | 50.0| 54.4  | 37.2   |\n| DriveTransformer        | 63.5| 35.0| 17.6  | 35.0     | 48.4   | 40.0    | 52.1  | 38.6   |\n| DriveAdapter            | 64.2| 33.1| 28.8  | 26.4     | 48.8   | 50.0| 56.4  | 42.1   |\n| TF++*                   | 76.9±0.9| 54.0±1.0| **48.8**±2.2| 37.6±7.0    | 64.2±8.4| 50.0±0.0| 59.7±6.1  | 52.0±3.0   |\n| GaussianFusion (Ours)      | **79.1**±1.1| **54.4**±2.6| 36.6±3.3  | **64.4**±2.3 | **66.5**±6.4   | **53.3**±5.8| **60.8**±6.4| **56.3**±3.7|\n\nOn the NAVSIM dataset, our method demonstrates low variance, indicating strong robustness to random initialization. On the closed-loop Bench2Drive benchmark, although the variance is relatively higher, our method still consistently outperforms baseline methods on average, highlighting its stability and effectiveness across diverse conditions.\n\nWe will include these aggregated results and variance estimates in the final version of the paper.\n\n>**Q3. The performance of Gaussian sparse representation on small and moving objects?**\n\nThe proposed 2D Gaussian sparse representation is capable of effectively capturing objects of various sizes, including small and dynamic ones, due to its **deformable and adaptive nature**. Unlike BEV-based dense representations, which may suffer from resolution constraints or fixed grid structures, our 2D Gaussians allow for flexible allocation of representation capacity to fine-grained details.\n\nAs shown in **Table 4**, our method achieves higher semantic map quality compared to BEV-based baselines. Furthermore, as demonstrated in the supplementary demo video, the 2D Gaussians successfully capture moving objects such as pedestrians and vehicles, indicating their effectiveness in dynamic driving scenes.\n\n>**Q4. How does or would the GaussianFusion perform under real-world challenges such as fog, occlusions, or sensor noise? Any plans to test beyond simulation?**\n\nWe appreciate the reviewer’s thoughtful question. The robustness of GaussianFusion under adverse weather conditions has been partially validated using the CARLA-based Bench2Drive benchmark, which includes diverse environmental settings such as **fog**, **rain**, and **cloudy skies**. As shown in the supplementary demo video, our method performs robustly in a foggy and rainy scenario, indicating strong adaptability to challenging visibility conditions.\n\nHowever, we have not explicitly evaluated the method under severe occlusions or sensor noise. We agree that assessing performance under these conditions is crucial for real-world deployment. We sincerely thank the reviewer for this insightful suggestion and will explore these factors in future work.\n\nRegarding real-world testing, due to the high cost and complexity of such experiments, we currently do not have plans to move beyond simulation. Nevertheless, we believe that the insights gained from simulation benchmarks like Bench2Drive provide a valuable proxy for many real-world challenges.\n\n>**Q5. Do the implicit and explicit branches ever conflict or interfere? How is their interaction managed during training?**\n\nWe did not observe any conflicts or interference between the implicit and explicit branches in our experiments. On the contrary, as shown in the **Table 3**, incorporating the implicit branch consistently improves performance, indicating that the two branches provide complementary information rather than competing signals.\n\nIn our current implementation, their interaction is managed by simply **concatenating their outputs** in the trajectory prediction module. While this approach proves effective in our setting, it is not necessarily optimal. We plan to explore more effective interaction mechanisms in future work.\n\n>**Q6. Table and figure captions lack clarity and exhibit inconsistent bolding.**\n\nThank you for your helpful comment. We will carefully revise all table and figure captions to improve clarity, ensure consistency in formatting, and enhance overall readability in the final version of the paper.\n\n>**Q7. The claim that GaussianFusion is more interpretable is kind of intuitive, but no formal interpretability analysis (e.g., user study, attribution) is provided, which could be beneficial for the contribution framing.**\n\nWe agree with the reviewer that our paper lacks a formal interpretability analysis. In this work, our primary focus is on validating the **effectiveness** of the GaussianFusion framework in the planning task.\n\nWe argue that the proposed 2D Gaussian representation is inherently more **intuitive** than flattened feature vectors or dense BEV grids. It allows for **visual inspection of spatial changes** during the feed-forward process, which provides a more direct understanding of what the model attends to in a scene.\n\nWe acknowledge that incorporating formal interpretability evaluations (e.g., attribution maps or user studies) could strengthen our contribution, and we plan to explore this direction in future work.\n\n>**Q8. Incorrect citation formatting: References should be ordered numerically and separated by commas.**\n\nThank you for your kind suggestion. We will carefully revise all in-text citations to ensure they are numerically ordered and properly formatted, following the required style in the final version of the paper.\n\n**References**\n\n[1] Kerbl B, Kopanas G, Leimkühler T, et al. \"3D Gaussian splatting for real-time radiance field rendering\". ACM Transactions on Graphics, 2023.\n\n[2] Huang Y, Zheng W, Zhang Y, et al. \"Gaussianformer: Scene as gaussians for vision-based 3d semantic occupancy prediction\". ECCV, 2024."}, {"review_id": "TWGZhKnNv6", "reviewer": "Reviewer_6QkV", "summary": "This paper introduces GaussianFusion, a novel Gaussian-based multi-sensor fusion framework for end-to-end autonomous driving. Existing methods often rely on flattened fusion or bird's-eye view (BEV) representations, which suffer from limited interpretability or high computational costs. The proposed framework innovatively uses 2D Gaussian distributions as an intermediate representation, initializing a set of Gaussians and iteratively refining them through multi-modal feature fusion. Explicit features capture scene semantics and spatial information, while implicit features are tailored for trajectory planning. The dual-branch fusion pipeline and cascade planning head further enhance scene understanding and trajectory optimization. Experiments on NAVSIM and Bench2Drive benchmarks demonstrate significant performance and robustness of GaussianFusion.", "questions": "1.\t3D Scene Extension: Can the current 2D Gaussian framework handle scenarios with vertical structures (e.g., viaducts, tunnels)? Are there plans to incorporate 3D Gaussians or hybrid representations?\n2.\tComputational Efficiency: Please provide inference time comparisons on embedded platforms (e.g., NVIDIA Jetson) to demonstrate real-world applicability.\n3.\tAblation Study Gaps: Could you include ablation results for the dual-branch structure and cascade planning head to quantify their contributions to EPDMS/PDMS metrics?\n4.\tDataset Limitations: Do NAVSIM and Bench2Drive cover extreme weather conditions? How robust is the framework under low visibility?", "limitations": "The authors do not adequately discuss the limitations of 2D Gaussians in complex 3D environments or the impact of sensor synchronization on fusion accuracy. Suggestions for improvement:\n1.\tClarify the theoretical boundaries of 2D Gaussian modeling, such as the effects of slopes and elevation changes on trajectory prediction.\n2.\tAnalyze how time synchronization errors between LiDAR and cameras affect Gaussian feature aggregation.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1.\tOriginal Architecture Design: First to introduce Gaussian representations to multi-sensor fusion for autonomous driving, leveraging the sparsity and physical interpretability (e.g., mean, scale, rotation) of 2D Gaussians to reduce computational complexity while improving scene representation transparency.\n2.\tTask-Specific Dual-Branch Mechanism: Decouples scene reconstruction (explicit branch) and planning guidance (implicit branch), enabling Gaussians to simultaneously model the environment and directly inform decision-making.\n3.\tEfficient Cascade Planning: Iteratively refines trajectories through hierarchical Gaussian queries, showing stronger stability in complex scenarios (e.g., lane-keeping, obstacle avoidance) with notable gains in sub-metrics like DAC and LK.\n4.\tCross-Benchmark Robustness: Outperforms existing methods in both open-loop (NAVSIM) and closed-loop (Bench2Drive) settings, validating generalization across diverse driving environments.\n\nWeaknesses\n1.\tLimited 3D Scene Adaptability: The 2D Gaussian assumption may not adequately handle complex 3D environments (e.g., ramps, overpasses), potentially restricting real-world applicability.\n2.\tIncomplete Computational Analysis: While claiming reduced overhead through sparsity, the paper lacks detailed comparisons with BEV methods in terms of computational efficiency, especially in real-time driving scenarios.\n3.\tInsufficient Ablation Studies: Fails to isolate the contributions of the dual-branch design and cascade planning head, making it difficult to quantify the impact of individual components.", "was_revised": false, "final_justification": "", "rebuttal": ">**Q1. Can the current 2D Gaussian framework handle scenarios with vertical structures (e.g., viaducts, tunnels)? Are there plans to incorporate 3D Gaussians or hybrid representations?**\n\nOur current 2D Gaussian framework primarily focuses on modeling foreground objects and road topology, which are critical for safe driving decisions. Since the output of the end-to-end planner is a 2D trajectory on the ground plane, we simplify the scene representation by assuming the ego vehicle operates on a relatively flat plane in its local coordinate system.\n\nAlthough extending our framework to support full 3D Gaussians or hybrid representations is technically feasible, such extensions would incur prohibitive computational costs that would undermine the system's real-time performance. Therefore, we currently do not plan to extend our framework with 3D Gaussian representations.\n\n>**Q2. The paper lacks detailed comparisons with BEV methods in terms of computational efficiency, especially in real-time driving scenarios.**\n\nThank you for highlighting this important aspect. We fully agree that computational efficiency is critical for real-time deployment.\n\nWe compare the inference latency of a representative BEV-based method and our approach on an NVIDIA RTX 3090 GPU, as reported in the **Table 4** of the paper. Our method achieves superior perception and planning performance while maintaining a lower inference latency of approximately **32 *ms***.\n\nGiven the unavailability of an embedded platform such as the NVIDIA Jetson AGX Orin, we conduct latency measurements on a desktop GPU (GTX 1080 Ti) as a proxy. This choice is justified by the fact that both hardware platforms exhibit similar computational capabilities for inference. Using the PyTorch implementation with float32 precision and without inference-specific optimizations, our model achieved an average inference time of **65 *ms***, which demonstrates the real-time applicability of our approach.\n\nWe acknowledge the importance of direct on-device benchmarking and plan to include such evaluations when the necessary hardware becomes available.\n\n>**Q3. Could you include ablation results for the dual-branch structure and cascade planning head to quantify their contributions to EPDMS/PDMS metrics?**\n\nThanks for the valuable suggestion. We conducted ablation studies to quantify the individual contributions of the dual-branch structure and the cascade planning head to the EPDMS metrics. The results are summarized in the table below:\n\n| Gaussian Exp. Fusion | Gaussian Imp. Fusion | Cascade Planning | Agent Pred. | Param. (M) | DAC↑ | TTC↑ | EP↑ | LK↑ | EPDMS↑ |\n|----------------------|----------------------|------------------|-------------|------------|------|------|-----|-----|--------|\n| ✗                    | ✗                     | ✗                | ✗           | 55.7       | 94.1 | 96.9 | 87.5| 96.2| 81.8   |\n| ✓                    | ✗                     | ✗                | ✗           | 49.6       | 96.5 | 97.1 | 87.8| 97.0| 84.2   |\n| ✓                    | ✓                     | ✗                | ✗           | 51.6       | 96.6 | 97.3 | 87.8| 97.3| 84.5   |\n| ✓                    | ✗                    | ✓                | ✗           | 53.7       | 97.0 | 97.2 | 87.4| 97.2| 84.4   |\n| ✓                    | ✓                    | ✓                | ✗           | 55.8       | 97.3 | 97.4 | 87.5| 97.4| 85.0   |\n| ✓                    | ✓                    | ✓                | ✓           | 59.5       | 96.2 | 97.3 | 87.6| 97.0| 83.8   |\n\nThe results show that adding the **Gaussian Explicit Fusion** branch alone (second row) significantly improves perception performance, with DAC increasing from 94.1 to 96.5 and EPDMS from 81.8 to 84.2 compared to the baseline without either branch. Adding the **Gaussian Implicit Fusion** branch independently (third row) further enhances these metrics slightly, raising DAC to 96.6 and EPDMS to 84.5.\n\nSeparately, incorporating the **cascade planning head** with only the explicit fusion (fourth row) also improves trajectory prediction, increasing LK and EPDMS compared to using explicit fusion alone. The best overall performance is achieved when combining dual-branch fusion and the cascade head (fifth row), reaching an EPDMS of 85.0. We will update these ablation results to Table 3 of the paper.\n\n>**Q4. Do NAVSIM and Bench2Drive cover extreme weather conditions? How robust is the framework under low visibility?**\n\nThank you for this insightful question. The Bench2Drive benchmark includes scenarios with extreme weather conditions such as heavy rain and dense fog, offering a realistic testbed to evaluate robustness under challenging environments.\n\nOur method demonstrates strong robustness in low-visibility conditions. As shown in the supplementary materials, a demo video illustrates our framework performing effectively in a scenario with dense fog and heavy rain. These results confirm that our approach can maintain reliable perception and planning performance despite adverse weather, underscoring its potential for real-world deployment in extreme conditions."}, {"review_id": "OqNYwdIOgs", "reviewer": "Reviewer_EPq1", "summary": "This paper proposes GaussianFusion, a novel multi-sensor fusion framework for end-to-end autonomous driving. Unlike traditional attention-based flatten fusion or BEV fusion methods, GaussianFusion uses 2D Gaussian representations as intermediate carriers to efficiently and interpretably integrate features from multiple sensors. The architecture includes a dual-branch fusion pipeline to capture local multi-sensor features and to aggregate global planning cues, respectively. Evaluations on NAVSIM and Bench2Drive benchmarks show that GaussianFusion achieves state-of-the-art performance with improved planning accuracy and efficiency, demonstrating the promise of Gaussian-based representations for autonomous driving systems.", "questions": "please see weaknesses", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n1. The overall structure of the paper is clear and easy to understand.\n\n2. The paper presents an efficient Gaussian-based multi-sensor fusion framework, and experiment results on both open-loop and closed-loop benchmarks validate its effectiveness.\n\n3. The paper provides extensive ablation studies to validate and analyze the proposed modules. \n\n**Weaknesses**\n\n1. Although authors state the differences compared to GaussianAD, the designs like multi-sensor fusion and 2D Gaussian cannot demonstrate advantages over GaussianAD. Besides, the authors seem not to demonstrate the necessity of using Gaussian representations. The proposed designs are not tailored for Gaussian representations, and can be easily integrated with other structures, like BEV-based methods. And the ablation in Tab.4 also shows that there doesn't appear to be a significant gap between Gaussian-based and BEV-based representations.\n\n2. Authors can provide some visualization results with more complex motion mode and some failure cases.", "was_revised": true, "final_justification": "Thanks for the authors' detailed responses. The advantages of Gaussian Fusion over previous methods are already clear, and my concerns have been addressed.", "rebuttal": ">**Q1. Concerns about the necessity and advantage of 2D Gaussian representations over existing methods.**\n\nThank you for the thoughtful comments. Our proposed **2D Gaussian framework** offers several key advantages over existing methods.\n\n**First**, compared to *GaussianAD* [1], our method significantly reduces the number of Gaussians required to model a driving scene by compressing 3D Gaussians into 2D representations (**25600** Gaussians in *GaussianAD* vs. **512** in ours). This leads to a substantially lower computational burden. Moreover, *GaussianAD* requires expensive **3D occupancy labels** for optimization, while our method only uses **2D semantic maps**—projected from road topology and bounding boxes onto the ground plane. These labels are widely available in existing driving datasets and can be more easily generated through automatic labeling pipelines.\n\n**Second**, compared to *BEV-based fusion methods* [2], our 2D Gaussian framework improves both **efficiency** and **accuracy**. Specifically, our method reduces inference latency by **25.6%**, while achieving **better performance in perception and planning**, as shown in Table 3 of the paper. In a typical BEV setup covering a range of `[-32m, 32m]` on both the x and y axes, a voxel size of `0.5m` results in a `[128, 128]` query map—i.e., **16,384** BEV queries. In contrast, our approach uses **only 512 deformable and position-adaptive 2D Gaussians**, which are far more compact and flexible in representing the scene compared to dense BEV grids.\n\n>**Q2. Authors can provide some visualization results with more complex motion modes and some failure cases.**\n\nThanks for your suggestion. Due to the limitations of the current rebuttal submission, we are unable to include visualization results here. We will include the relevant visualizations—covering both complex motion scenarios and failure cases—in the appendix of the final version.\n\n**References**\n\n[1] Zheng W, Wu J, Zheng Y, et al. \"Gaussianad: Gaussian-centric end-to-end autonomous driving\". arXiv preprint arXiv:2412.10371, 2024.\n\n[2] Li Z, Wang W, Li H, et al. \"Bevformer: learning bird's-eye-view representation from lidar-camera via spatiotemporal transformers\". IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024."}, {"review_id": "n0Azgu7iNQ", "reviewer": "Reviewer_e6dC", "summary": "Current end-to-end driving methods handle perception and sensor fusion by either geometrically projecting encoded sensor features into a BEV representation or implicitly mapping features to a 2D grid via global attention.\nThis paper instead proposes to use a point based 2D Gaussian intermediate representation upon which all features are mapped. The paper then proposes a refinement pipeline to convert the Gaussian features to planning outputs.\nThe method is evaluated on Bench2Drive and NavSim.", "questions": "L. 269: Cropping the camera image to only 448 × 250 (is it HxW or WxH?) seems to be too small to me. For comparison, TF++ uses (384x1024 HxW). Are multiple cameras being used here? Or do the authors have any intuition why such a small camera was sufficient for Bench2Drive?\n\nL. 311: How are the actions of the car computed if the model prediction head is removed?\nIs the whole model architecture trained in one stage, or is the vision backbone trained separately with semantic mapping?\n\nThe 77.2 DS result of TF++ result in Table 2 is marked as using the same backbone and training dataset as GaussianFusion.\nTF++ reports 84.2 DS performance in the draft using a regnety_032 backbone.\nThe training dataset used in this work seems to be the same dataset as used in TF++, except that only the town 12 subset of the data was used.\nSo is the lower performance of TF++ a result of using less data and a smaller backbone?\nThe description of Table 2 should explicitly state that the other baselines besides TF++ were trained using a different dataset (Bench2Drive) than GaussianFusion and TF++. This is fine but should be said explicitly.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper investigates a new representation for sensor Fusion 2D-Gaussians in BEV. This is interesting in particular because Gaussians have been so successful in NVS / 3D reconstruction. The paper follows the standard recipe of proposing a method, comparing its performance against baselines, and ablating components.\nI particularly appreciate the choice of using a combination of NavSim and Bench2Drive to assess the performance of the method. This measure performance with realistic sensor data (NavSim) with a good metric as well as closed-loop performance (Bench2Drive) both for short driving periods.\n\nL. 82: “significantly surpassing current state-of-the-art methods.” The state-of-the-art (of prior work) on NavSim is Hydra-MDP-C with 91.0 PDMS. Since this method achieves 88.9 PDMS it does not surpass the state of the art, so the claim is incorrect. However, this paper uses a lightweight vision backbone, so I recommend making some claim around high performance with low inference time instead, or making a claim around surpassing the state-of-the-art in methods that use ResNet34 as vision backbone. \n\n[1] Could additionally be cited when discussing BEV fusion methods for E2E driving.\n\nTable 1 does not make it clear that only baselines using the ResNet34 backbone are shown, and better methods like Hydra-MDP++ with the V2-99 backbone are omitted.\n\nThe EPDMS is a metric from the NavSim v2 benchmark that uses 2 stages. This paper uses this metric with the NavSim v1 benchmark and seems to alter the metric by using only 1 stage. It is not clear to me why the EPDMS metric is used with NavSim v1, it does not seem to provide additional insights compared to the standard PDMS metric.\nI recommend the authors change Table 1 to use the standard PDMS metric (which is in Appendix Table 5), for which there are also more baselines available.\nI also recommend that more baselines be added to the table and that the author include the SOTA, like Hydra-MDP-C and Hydra-MDP++ (V2-99). The methods could, for example, be grouped by the image backbone being used to make it clear that some of the better methods use larger image backbones (and compare GaussianFusion within the ResNet34 group).\n \nTraining end-to-end driving methods can exhibit quite some variance. Both Tables 1 and 2 would benefit from evaluating multiple (3 is typical) training seeds and reporting the mean and standard deviation. NavSim is deterministic, but Bench2Drive is not, so multiple evaluation seeds (3) would also be better here.\n\nL. 307: The paper claims here that the method does not significantly increase model complexity because the number of parameters is not increased. This argument would be more convincing if, additionally, the number of FLOPS used or inference time were also reported, as they might increase with the iterative processing of Gaussians. Table 4 suggests that compute requirements do increase. The paper claims that this is due to worse cuda kernel optimization. This argument could be more convincing if the number of flops were reported.\n\nThe examples shown in Figure 4 do not seem particularly interesting. The first example is at the end of a left turn, where the car just has to follow the lane. The second and third examples seem to be basic straight driving. \nFigure 4 could be moved to the appendix if more space is needed in the main paper.\n\nThe 2 sentence limitations in the conclusion  seem to be too brief. There are probably more limitations to this study. These can perhaps be expanded in the appendix if space is a concern.\n\nOverall, I appreciate the study of using 2D Gaussians for sensor fusion. I am concerned that the experimental section focuses more on selling the method than educating the reader about its advantages and disadvantages. The appropriate state-of-the-art methods should be acknowledged in the table comparisons. If the paper wants to claim state-of-the-art performance, it should train GaussianFusion with better vision backbones and show that it can actually achieve state-of-the-art numbers. Otherwise, the claims should be toned down and made specific to the ResNet34 backbone.\nI would consider raising my score if this is addressed.\n\nReferences:\n\n[1] Anthony Hu, Gianluca Corrado, Nicolas Griffiths, Zak Murez, Corina Gurau, Hudson Yeo, Alex Kendall, Roberto Cipolla, Jamie Shotton: “Model-Based Imitation Learning for Urban Driving”, NeurIPS 2022", "was_revised": true, "final_justification": "My concerns have been adressed in the rebuttal.\nI update my rating to accept.", "rebuttal": ">**Q1. Additionally experiments about V2-99 vision backbone.**\n\nThank you for your helpful suggestion. To explore the **scalability** of our framework, we extended *GaussianFusion* by applying a more powerful image backbone (**V2-99**) and increasing the dimension of Gaussian feature from 128 to 256 to adapt to V2-99. The results are shown in Table 1 below.\n\nAs we can see, our enhanced version (**GaussianFusion\\***), equipped with V2-99, further improves performance across all metrics—achieving state-of-the-art results on the **Navtest** benchmark. This demonstrates the scalability of our framework with stronger backbones.\n\nWe note that, due to the tight rebuttal timeline, we were only able to perform **a single-seed training run** for this extended version. Nevertheless, the results already show clear performance gains. The results will be updated to **Table 1** of the paper for comprehensive comparison.\n\n**Table 1. Performance on the Navtest Benchmark.** ‘*’ denotes an extended version of our method.\n\n| Method               | Input   | Img. Backbone | NC ↑  | DAC ↑ | TTC ↑ | EP ↑  | PDMS ↑ |\n|----------------------|---------|---------------|-------|-------|-------|-------|--------|\n| LTF                  | Camera  | ResNet34      | 97.4  | 92.8  | 92.4  | 79.0  | 83.8   |\n| TransFuser           | C & L   | ResNet34      | 97.7  | 92.8  | 93.0  | 79.2  | 84.0   |\n| GoalFlow             | C & L   | ResNet34      | 98.3  | 93.3  | 94.8  | 79.8  | 85.7   |\n| Hydra-MDP            | C & L   | ResNet34      | 98.3  | 96.0  | 94.6  | 78.7  | 86.5   |\n| Hydra-MDP++          | C       | ResNet34      | 97.6  | 96.0  | 93.1  | 80.4  | 86.6   |\n| ARTEMIS              | C & L   | ResNet34      | 98.3  | 95.1  | 94.3  | 81.4  | 87.0   |\n| DiffusionDrive       | C & L   | ResNet34      | 98.2  | 96.2  | 94.7  | 82.2  | 88.1   |\n| **GaussianFusion (Ours)**     | C & L   | ResNet34      | 98.3  | 97.2  | 94.6  | 83.0  | **88.8**   |\n|                      |         |               |       |       |       |       |        |\n| GoalFlow             | C & L   | V2-99         | 98.4  | 98.3  | 94.6  | 85.0  | 90.3   |\n| Hydra-MDP-C          | C       | V2-99         | 98.7  | 98.2  | 95.0  | 86.5  | 91.0   |\n| Hydra-MDP++          | C       | V2-99         | 98.6  | 98.6  | 95.1  | 85.7  | 91.0   |\n| **GaussianFusion\\* (Ours)**   | C & L   | V2-99         | 98.7  | 98.1  | 95.7  | 88.2  | **92.0**   |\n\n>**Q2. Why the EPDMS metric is used with NavSim v1?**\n\nThank you for the question. We adopt **EPDMS** because it is a **more challenging and comprehensive evaluation metric** than PDMS. Originally proposed by *Hydra-MDP++* [1], EPDMS extends the standard evaluation protocol by introducing several additional criteria:\n\n- **Lane Keeping (LK)**\n- **Extended Comfort (EC)**\n- **Driving Direction Compliance (DDC)**\n- **Traffic Light Compliance (TLC)**\n- **False-Positive Penalty Filtering**\n\nThese components enable a more holistic assessment of driving behavior. Importantly, while EPDMS is employed by *NavSim v2*, it is also compatible with **NavSim v1** for single-stage evaluation.\n\nWe agree with the reviewer that only a limited number of existing methods have been evaluated under EPDMS, which may affect direct comparability. Therefore, following your suggestion, we will move the EPDMS results to the Appendix in the final version.\n\n>**Q3. Training end-to-end driving methods can exhibit quite some variance. Both Tables 1 and 2 would benefit from evaluating multiple (3 is typical) training seeds and reporting the mean and standard deviation.**\n\nThanks for your helpful suggestion. We have trained models under 3 training seeds on both the NAVSIM and Bench2Drive benchmarks. As the evaluation on the CARLA-based Bench2Drive benchmark is very time-consuming, one trained model is only evaluated once. Due to the limitation of character count, please see the results in Tables 1 and 2 of the response to the Reviewer v3h9.\n\nOn the NAVSIM benchmark, our method exhibits **stable performance with minimal variance**, reflecting its **robustness to random initialization** and consistent behavior across multiple runs. \n\nFor the closed-loop **Bench2Drive benchmark**, while slightly higher variance is observed—as expected due to the complexity and stochastic nature of interactive scenarios—our method **consistently surpasses other baselines in average performance**. These results will be updated to the final version of the paper.\n\n>**Q4. Reporting FLOPs to better show the computational efficiency.**\n\nAccording to your suggestion, we have calculated the FLOPs of different fusion methods. The results are shown in Table 2 below.\n\n**Table 2. Comparison of different fusion methods on accuracy and efficiency.**\n| Fusion Method | Param. | mIoU↑ | EPDMS↑ | FLOPs (G) | Latency (ms)↓ |\n|---------------|--------|--------|-------|--------|---------------|\n| Flatten       | 55.7M  | 0.50  | 81.8     | 27.4     | 18   |\n| BEV           | 51.9M  | 0.51  | 83.8  | 58.4      | 43  |\n| Gaussian      | 51.6M  | 0.55  | 84.5    | 35.7      | 32 |\n\nCompared with the BEV fusion method, our Gaussian fusion achieves better performance (+0.04 mIoU and +0.7 EPDMS), while also significantly reducing computational cost: the FLOPs are 38.9% lower (58.4G → 35.7G) and latency is reduced by 25.6% (43ms → 32ms), showing clear advantages in both accuracy and efficiency.\n\nCompared with the Flatten (TransFuser-style) fusion, which is a very lightweight approach, our method exhibits only a 30.3% increase in FLOPs (27.4G → 35.7G), while achieving much stronger performance (+0.05 mIoU and +2.7 EPDMS). However, our method's latency is 77.8% higher (18ms → 32ms), which we believe is largely due to the differences in operator-level optimization. This could be further mitigated through engineering improvements in deployment.\n\n>**Q5. The examples shown in Figure 4 do not seem particularly interesting. The first example is at the end of a left turn, where the car just has to follow the lane. The second and third examples seem to be basic straight driving. Figure 4 could be moved to the appendix if more space is needed in the main paper.**\n\nThanks for your suggestion. We will move Figure 4 to the appendix and include additional visualizations of more complex scenarios and failure cases in the final version of the paper.\n\n>**Q6. The 2 sentence limitations in the conclusion seem to be too brief. There are probably more limitations to this study. These can perhaps be expanded in the appendix if space is a concern.**\n\nThank you for pointing this out. We agree that the limitations section in the conclusion is overly concise and does not sufficiently reflect the boundaries of our study. In the final version, we will include a dedicated Limitations section in the appendix to provide a more comprehensive discussion. \n\nBased on the reviewer’s suggestion and further reflection, one important limitation is that we have not evaluated the robustness of our fusion method under sensor occlusion or noise, which is a critical aspect for real-world deployment. \n\nAnother limitation is that our current design relies on 3D bounding boxes and road topology annotations to optimize 2D Gaussians. While effective, such supervision can be expensive or unavailable in real-world deployment scenarios. \n\nWe appreciate the reviewer’s input in helping us better contextualize the scope of our work.\n\n>**Q7. Citing a BEV method MILE [1] for E2E driving.**\n\nThank you for pointing this out. MILE [1] is a pioneering work in BEV-based end-to-end driving. It lifts image features into 3D space by leveraging a predicted depth probability distribution and then aggregates the resulting voxel features into the BEV space via a predefined grid-based sum-pooling strategy. We appreciate the reviewer’s suggestion and will include a citation and discussion of MILE in the related work section of the final version.\n\n>**Q8. About the image resolution setting.**\n\nThank you for pointing this out. We acknowledge that the resolution setting was not clearly described in the manuscript. The resolution of 448 × 250 (W×H) is used on the NAVSIM benchmark, where multiple camera views are concatenated. For the Bench2Drive benchmark, we adopt only the front-view camera, which already provides a wide field of view. In this case, we use the resolution of 1024 × 384 (W×H), which is consistent with the setting used in TransFuser++.\n\nWe will clarify this resolution setting and correct the description in the final version of the paper.\n\n>**Q9. About training of the GaussianFusion framework.**\n\nIn our framework, the perception head (used for map construction) and the planning head (used for trajectory prediction) are designed to be independent branches. The perception head does not contribute directly to the driving actions; rather, it serves as an auxiliary supervision signal to optimize 2D Gaussians and build geometry inductive biases.\n\nAs for the training strategy, our model is trained in a single-stage end-to-end manner, without any separate pretraining of the perception head.\n\n>**Q10. About the training settings on the Bench2Drive benchmark.**\n\nWe believe the lower performance of TF++ in our experiments can indeed be attributed to the factors: the smaller model capacity and the reduced training data.\n\nSpecifically, the original TF++ paper utilizes RegNetY-32 as the backbone and is trained on a dataset that is roughly three times larger than what we used in our experiments. In contrast, our reproduced version of TF++ adopts a lighter-weight backbone (for fair comparison) and is trained from scratch with a smaller training split (due to the computing power limitation). \n\nAccording to your suggestion, we will explicitly state the differences about the training datasets in the caption of Table 2 of the paper.\n\n**References**\n\n[1] Hu A, Corrado G, Griffiths N, et al. “Model-Based Imitation Learning for Urban Driving”. NeurIPS, 2022."}]

Author rebuttal:

Meta-review: This paper proposed a multi-sensor fusion framework for end-to-end autonomous driving based on 2D Gaussian representation. Experiments were conducted on NAVSIM and Bench2Drive to validating its planning performance for autonomous driving.
After the rebuttal and author-review discussion phase, all the reviewers reached the consensus to accept the paper, based on its contribution about proposing a new fusion framework beyond existing BEV or attention-based ones. After reading the paper, reviews, authors’ feedbacks and discussions, the AC agree with the reviewers to recommend accept this paper.

Since the proposed new fusion framework would provide new insights for multi-sensor fusion, not restricting to autonomous driving, the AC would like to recommend spotlight.
Decision: Accept (spotlight)