DeltaFlow: An Efficient Multi-frame Scene Flow Estimation Method
Authors: Qingwen Zhang
Xiaomeng Zhu
Yushan Zhang
Yixi Cai
Olov Andersson
Patric Jensfelt
Venue: NeurIPS 2025 spotlight ()
Keywords: Scene flow estimation
Point clouds
Efficient and scalable vision
Primary area: applications

Abstract: Previous dominant methods for scene flow estimation focus mainly on input from two consecutive frames, neglecting valuable information in the temporal domain. While recent trends shift towards multi-frame reasoning, they suffer from rapidly escalating computational costs as the number of frames grows. To leverage temporal information more efficiently, we propose DeltaFlow ($\Delta$Flow), a lightweight 3D framework that captures motion cues via a $\Delta$ scheme, extracting temporal features with minimal computational cost, regardless of the number of frames. Additionally, scene flow estimation faces challenges such as imbalanced object class distributions and motion inconsistency. To tackle these issues, we introduce a Category-Balanced Loss to enhance learning across underrepresented classes and an Instance Consistency Loss to enforce coherent object motion, improving flow accuracy. Extensive evaluations on the Argoverse 2, Waymo and nuScenes datasets show that $\Delta$Flow achieves state-of-the-art performance with up to 22\% lower error and $2\times$ faster inference compared to the next-best multi-frame supervised method, while also demonstrating a strong cross-domain generalization ability. The code is open-sourced at https://github.com/Kin-Zhang/DeltaFlow along with trained model weights.

Fllow: An Efficient Multi-frame Scene Flow Estimation Method
Qingwen Zhang 1,50
Xiaomeng Zhu 13
Yushan Zhang
Yixi Cai Olov Andersson
Patric Jensfelt
KTH Royal Institute of Technology gingwer&kth.se, yushan. thang@liu...
LLinköping University
SSannia CV AB
Abstract
Previous dominant methods for scene flow estimation focus mainly on input from Iwo consecutive frames, neglecting valuable information the temporal domain. While recent trends shift towards multi-frame reasoning, they suffer from rapidly escalating computational costs as the number of frames grows. To leverage tem- poral information more efficiently, we propose DeltaFlow (AFlow), lightweight 3D framework that captures motion cues via A scheme, extracting temporal features with minimal computational cost, regardless of the number of frames. Additionally, scene flow estimation faces challenges such as imbalanced object class distributions and motion inconsistency. To tackle these issues, we introduce a Category-Balee Balanced Loss to enhance learning across underrepresented classes and Instance Consistency Loss enforce coherent object motion, improving flow accuracy. Extensive evaluations on the Argoverse 2, Waymo and nuScenes datasets show that AFlow achieves sate-of-the-art performance with up to 22% lower error and 2 x faster inference compared to the next-best multi-frame supervised method, while also demonstrating strong cross-doman generalization ability. The code is open-sourcee at atlat talattps:: htt////ittbbb/ com/ Kin- Zhang/ DeltaFlos along with trained model weights.
1
Introduction
Scene flow estimation determines the 3D motion of each point between consecutive point clouds, making it an important task in computer vision and essential for autonomous driving [1
43
and motion compensation 88 46). While early approaches focused on per-point feature learning
4g
27 25 26 48 44) and achieve high accuracy on small-scale datasets, they become computationally
expensive when processing large-scale, high-density point clouds typical in autonomous driving. To reduce computational costs and enable real-time inference, recent methods [15 voxelize point features estimate the scene flow vector field.
18
Meanwhile, real-world LiDAR data acquired as a continuous stream rather than isolated frame pairs, making it crucial to leverage temporal information from multiple frames for more accurate motion estimation. To incorporate temporal information, existing multi-frame approaches either concatenate voxel features along the feature dimension [1] 44
(see (igure I[a)), introduce an
explicit temporal dimension to stack them 28 [8] (see Figure lb)). Both strategies lead increased
feature size and network parameters as the number of frames increases, resulting in higher memory consumption and slower training and inference.
To address these limitations, propose DeltaFlow (AFlow), computationally efficient 3D frame- work for multi-frame scene flow estimation. It applics a direct A scheme between voxelized frames, shown in Figure T(c), avoiding the feature concatenation 4D stacking used by prior methods in
Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Multi-free frami Point Clouds
(a) Concatenate
(b) 4D
(c) A (Ours)
Schame
M
+
M
M
M
M
M;
M
Irgatt: Fiotture Sire:
P M
M
X X NC
XXYXZXXXN
X XXXxXXX
strategies for scene flow estimation. For clarity, voxelized features are shown in dense formats. X, Y, Z denote spatial resolution, C' represents feature channels, and N the number of frames. Existing methods process voxelized representations using (a) Concatenation features along the channel dimension [4 15]; (b) 4D methods stack features in an additional temporal dimension [8 28 Both increase input size as N grows. (c) Our proposed
Figure Comparison of
AFlow applies a A scheme between voxelized frame, maintaining a compact feature representation and a constant feature size independent of N.
Figure Πa), (b). The scheme allows the network to focus on "what is changing" in the scene rather than the static background, aligning with the core objective of scene flow estimation. It also keeps the input feature size of AFlow constant regardless of the number of frames, effectively addressing the scalability challenge in multi-frame scene flow estimation.
We further propose improvements the scene flow supervision signal. Existing approaches [44] 15 34] for driving scenarios primarily focus on distinguishing between static and moving objects. However, they do not explicitly address severe class imbalances (e-g., cars versus pedestrians) as mentioned in [16), nor ensure motion consistency across all points within the same object. To tackle these issues, we propose a Bentegory-Balancee Loss achieve more balanced training across all the classes, including the underrepresented classes (e.g., pedestrians, cyclists), and an Instance Consistency Loss to enforce uniform motion for each individual instance.
AFlow achieves the best performance for real-time scene flow estimation on Argoverse 2, Waymo and nuScenes datasets, outperforming the next-best multi-frame supervised method by up to 22%. It also demonstrates high computational efficiency and scalability in multi-frame settings, achieving up 2x faster inference, and exhibits strong generalization ability across different datasets. With its accuracy and efficiency, Flow is well-suited for real-world autonomous driving applications. The contributions of this paper are as follows: (1) We propose AFlow, lightweight 3D framework for multi- faalie-frame scene flow estimation that efficiently extracts motion cues by a A scheme between voxelized frames, maintaining a compact feature representation that is scalable in the temporal domain. (2) We introduce Category-Balanced Balanced Loss and an Instance Consistency Loss to enhance dynamic flow for underrepresented classes and improve motion consistency for individual instances. (3) We demonstrate that AFlow achieves state-of-the art real-time performance on three datasets, while exhibiting high computational efficiency and strong cross-domain generalization ability.
2
Related Work
Scene Flow Estimation
Scene flow estimation describes the 3D motion field between temporally successive point clouds [36] 23 41 49). Early methods focused on point-wise feature learning [38
20 37 25
49], achieving high accuracy on small-scale synthetic datasets such as ShapeNet [6]
and Flying 3DDn 29] However, when applied to large-scale, high-density point clouds typical in autonomous driving
5 10), these methods require downsampling due to high memory costs and are not well optimized for sequential data, limiting their practical utility.
33 30
To handle large-scale point clouds, FastFlow3D [15] voxelized point clouds and concatenated voxelized features from two frames before feeding them into the network. However, voxelization sacrifices fine- fine-grained motion details, as point-to-voxed transformations reduce spatial resolution, thereby diminishing accuracy at the object level. DeFlow [44] addressed this by introducing GRU-

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based sexel-to-point refinement, while SSF 17 leveraged sparse convolutions and virtual voxels to enhance long-range scene flow estimation.
Multi-frame challenges Multi-frame modeling has become a key trend in scene flow estimation, as leveraging past frames provides richer temporal context and allows for more comprehensive understanding of motion dynamics over time [8] [5]. One approach is to process all frames in sequence offline, as demonstrated by EulerFlow B5 Although it achieves high accuracy, it highly computationally demanding, requiring 24 hours to process sequence of 157 frames in Argoverse 2, making infeasible for real-time applications. An alternative is to concatenate
features, as done by most voxelized methods mentioned earlier. However, this leads to feature expansion, higher memory consumption, and limited temporal consistency as more frames are added.
To improve efficiency, two common strategies are used: 1) spatial optimization and 2) temporal optimization. For spatial optimization, methods in [15 17 reduce spatial dimensions by com- pressing the Z-dimension into a bird's- s-eye view (BEV) representation, effectively transforming the network into 2D processing. While this reduces the computational cost, it removes height information, which may degrade accuracy. Alternatively, Kim et al. [8]] applies sparse voxelization, using storage formats like coordinate format (COO) to store only nonzero elements with an indices matrix for coordinates and a value array for features. This efficiently reduces memory consumption while preserving the full 3D structure. For temporal optimization, Kim et al. [88] introduces an explicit temporal dimension, avoiding direct feature concatenation across frames. Instead of increasing feature channels, it proposes a 4D network with separate 3D spatial and 1D temporal convolutions, scaling input size multiplicatively with the number of frames. This reduces feature expansion and enhances the feasibility of multi-fran framef processing.
In this work, we also enhance spatial efficiency with sparse voxelization, preserving 3D structure while reducing memory usage. For temporal efficiency, introduce A scheme that extracts motion cues without expanding feature size, addressing scalability challenges in multi-frame scene flow estimation.
Other challenges Beyond computational challenges, scene flow estimation is further complicated by label imbalance. Most LiDAR points in autonomous driving scenarios belong to static structures such as buildings or roads, while dynamic objects are comparatively scarce. This imbalance biases model learning, making motion variations harder capture. Prior works [44
attempt to mitigate this issue using scaling functions loss design to balance motion contributions. Among them, the motion-aware loss from DeFlow 44 which applies unweighted three-speed ranges, has shown the most effectiveness.
13 34 45)
However, category imbalance remains challenge. The recent scene flow evaluation metric [16] highlights that small but safety-critical categories, such as pedestrians and cyclists, are underrepre- sented compared to larger vehicle classes, making mmlll-nnttance predictions challenging. Meanwhile, Zhang et al. [45] emphasize the need for object-level motion consistency, where instances within the same object should share coherent scene flow. To address these issues, we introduce Category- Balanced Loss and Instance Consistency Loss in this paper.
Method
3.1 Problem Formulation
Given consecutive point clouds, Pi-1 RRN--i3 and P, RNNx3 scene flow estimation aims to predict how the points pt-1 E P.-1 move from time 1- 1 to f, resulting in a scene flow vector field Fi-1 E N The estimated flow f: from P:-1 to P. can be decomposed as:
F=go + +AF
(1)
where Fego represents the motion caused by the ego vehicle. This motion is computed from the relative transformation of the sensor pose To between time t - and i.c., Fego T Ti-1-(p,_ Pt-1- Since Fego can be determined directly from odometry, the goal estimate the residual scene flow A with our approach.
Most existing scene flow estimation methods focus reasoning with two consecutive point cloud frames 21
22 4 13 17), learning a mapping: (T I 1-xt
Pr P.)) + AFF With the re- we instead focus on learning: p1-1--1p,11, Pt] + AF, to leverage additional past frames for improved
ago
cent trend shifting towards multi-frame reasoning
18
46 35
(T--N-P, -P,,,,,.... ego motion estimation.
3

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F
n
Loss: mobion + category + instance
g
N
Dáelca
Decoder
MUP
9
A A
g
P
A
Point Feature Extraction
Sparse Voxel Festures
Inpat
Temporal & Scheme (Eq.3)
3D backbone
Output AFF-1
Figure 2: Overview of the proposed AFlow architecture. The framework first extracts point-level features and voxelize them to obtain sparse voxel features 9. The core temporal scheme then computes the difference between the current frame t and previous frames (t (t-1) 1,...-.. ..... N-N,, weighted by a time-decay factor X. The resulting A feature Ddetu is then passed to 3D backbone -accbone-decoder decoder network to estimate the final scene flow A.F--1. This approach captures motion-specifi cues efficiently while keeping the architecture compact and scalable, regardless of the number of frames.
3.2 AFlow
To effectively learn multi-frame information, we propose AFlow, as shown in Figure 2 We extract sparse A feature that efficiently encodes temporal and spatial information from the frames, then feed into standard backbone-decoder network for scene flow estimation.
Point Feature Extraction Following common practices in scene flow estimation 15
18 we
first encode individual point clouds using PointPillars [19,, generating point-wise feature representa- tions ( F, Fe). Each F, NR.N represents the feature embedding for P,, where N₂ is the number of points and is the feature dimension.
Sparse Spatial Representation We then encode the point features into a sparse 3D representation, which processes only non-empty voxels to reduce computational overhead in large-scale 3D grids. Given encoded point features F NexC we construct sparse voxel features D E RVxC through point-to-voxel aggregation:
Σ
Epep', Fp P
Uj E V,
[1]]
otherwise,
where v; (xi, yi, z)) denotes the i-th active voxel coordinate in (the of non-empty voxels with [V| = V). p represents points inside voxel and f. E RC is the feature of point
Temporal Scheme order extract motion signals from the sparse voxel features, we propose simple yet effective A scheme comprising subtraction, temporal weighting and summation steps:
N X"11 -21---111)
Delti
Σ
resulting the A feature Daeta VxC, . the number of past frames considered, and applies temporal decay to earlier frames.
The scheme is designed to extract global motion patterns from multiple frames while maintaining computational efficiency. First, voxel-wise differences between the current frame and previous ones computed, encouraging the model to focus what is changing in the scene while minimizing reliance on static features. These differences are then weighted by a decay factor À E (0. 1], which assigns higher importance to more recent frames. The weighted differences are subsequently summed to accumulate the trail of moving objects and produce temporal representation that captures long- term motion information. The intuition this accumulation is to mimic how humans can interpret motion in single image from motion blur. We provide qualitative support for the design of the A scheme in [ecciin 5.5] which illustrates the temporal behavior of the proposed method and highlights its emphasis motion-related changes.

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Notably, this scheme maintains constant feature dimension, ensuring that the feature size remains unaffected by the number of frames. This allows the model to process an arbitrary number of past frames without increasing computational overhead in the backbone-decoder network.
Backbone-Decodee network The A feature detta is then served as input to 3D backbone-decoder network for scene flow estimation. is first processed by 3D backbone for feature extraction:
(out)
Backbone
Ddetm:
W not
where Backbone refers to any network capable of processing sparse 3D voxel inputs, and W net trainable network parameters. The backbone output (out) then sent to scene flow decoder network to estimate a per-point 3D scene flow vector:
AF Decoder (oun) Ft-1;; Wa),;
where the mapping V2P (out)) RVxC + R xO maps features back to points via pre-recorded coordinate indexing, and W d are trainable decoder weights.
3.3 Loss Function
We employ three loss functions to supervise scene flow estimation: the motion-awareness loss from DeFlow [44], and two new ones proposed in this work, a balegory-balanced loss and an instance consistency loss, that address class imbalance and motion inconsistency.
Motion-awareness Loss The motion-awarenen awareeess loss Ldetow from DeFlow is designed to mitigate data imbalance between static and dynamic points by prioritizing dynamic point flow estima- tion. It categorizes points in P. based on their motion speed into three groups] (Pt/1, P1/2. P1/a). resulting in the loss:
Liellow
Σ (Pe/ll pEP...
|AF -
Category-Balancee Loss The Category-Balances Loss is designed categorize dynamic objects based class and motion speed, ensuring a more balanced scene flow learning across different object categories. To achieve this, we assign to each point p a meta-category from the set C, with each category assigned predefined weight We- The loss is then defined as:
Lo
Σ
We
70
Σ
(6)
Po.h
BEB
pEP
where 76 are speed-dependent coefficients that adjust the weighting based on motion speed.
Instance Consistency Loss The instance consistency loss designed ensure that all points rigid object exhibit a consistent scene flow. To achieve this, we let I be the set of object instances, and for each instance I E I, let Pr denote the set of points belonging to The per per-instance average estimated error is defined as:
AF (p)l22 P
ê = Σ
PEP
Each instance is assigned a representative meta-category çı, and only moving instances (I') where speed exceeds 0.4 m/s are considered. The loss is then defined as:
C,
We, è exp (ê1).
I
The final loss function is the sum of all three losses:
Listll = Latetow Lo + Lr-
DeFlow loss categorizes motion speed into three groups B: 0 to 0.4 m/s. 0.4 to 1.0 m/s, and above 1.0
m/s, respectively.
5

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Experiments Setup
4.1 Datasets
Experiments are conducted on three commonly used large-scale autonomous driving datasets in scene flow estimation: Argoverse (39), which employs two roof-mounted 32-channel LiDARs: Waymo [33), which uses single 64-channel LiDAR; and nuScenes [5], which uses a 32-channel
LiDAR. Ground removal is applied Argoverse 2 and Waymo using HDMap information follow-
ing [34), and to nuScenes using line-fi fit ground segmentation [12].
Argoverse provides an official public scene flow challenge D1 consisting of 700 training and 150 validation scenes, each lasting 15 seconds 10 Hz, totaling 110,071 point cloud frames. An additional 150 test scenes are available for eval- uation via the online leaderboard. The scene flow ground truth is generated from human annotations with tracking-based inference to estimate 3D motion. However, noted in [46], non-ego motion distortion can lead to inaccurate annotations, as points from fast-moving objects may fall outside their labeled bounding boxes. To address this issue, we follow the velocity- -warr annotation refinement strategy in [46], which enlarges the bounding box of each object along its motion direction to include all distorted points. As illustrated in Figure 3] the 3D flow vectors (red lines) accurately capture the true motion of previously dis- torted points.
(a) Before
(b) After
Figure 3: Comparison scene flow ground truth
before and after motion compensation on a high- speed car. Blue points: LiDAR scan at t++ 1; Green points: LiDAR scan at t; Red lines: annotated flow vectors.
Waymo 15
contains 798 training and 202 validation sequences, each recorded at 10 Hz for around 20 seconds. The training set consists of 155,000 frames. Motion distortion affects both the point cloud and ground truth. However, direct annotation refinement is infeasible as it does not provide per-point timestamps. Thus, evaluation is conducted using the original annotations.
33
nuScenes [5] includes 700 training and 150 validation scenes, each recorded at 20 Hz for around 20 seconds. The training set contains 275,150 frames, which 27,392 (=100% are annotated with ground-truth labels, yielding effective annotation rate of 2 Hz. For consistency with Argoverse 2 and Waymo, we downsample the LiDAR data to Hz, yielding a standard 100 ms interval between consecutive frames. Ground-truth scene flow is constructed by computing rigid transformation for each object from its annotated 3D bounding box and velocity, then applying this transformation to all points within the object to obtain flow vectors.
4.2 Evaluation Metrics
The leaderboard I evaluates scene flow using two metries: three-way End Point Error (EPE) and Dynamic Bucket-Normalized EPE. EPE is defined as the L.2 norm of the difference between predicted and ground truth flow vectors, measured in centimeters. Threc-way EPE 7 computes the unweighted average EPE over three regions: foreground dynamic (FD), foreground static (FS), and background static (BS). point is classified as dynamic its ground truth velocity exceeds 0.5 m/s, and foreground if it lies within the bounding box of any tracked object. Dynamic Bucket-Normallin EPE [6] groups point into predefined motion buckets based on their speeds and normalizes EPE Mean EPE This metric evaluates four object categories: regular cars (CAR), other by mean speed Mean speed
vehicles (OTHER) such trucks and buses, pedestrians (PED), and wheeled vulnerable road users (VRU), including bicycles and motorcycles.
4.3 Implementation Details
3D backbone, widely used sparse convolutional network known for strong performance in 3D perception tasks. The scene flow decoder follows DeFlow [44) enabling effective per-point scene flow prediction. Further details the A scheme and the full 3D backbone-decoder architecture are provided in Appendix A.I
In implementation, adopt MinkowskiNet 99
For Argoverse 2, test set results are obtained directly from the public leaderboard 1 to ensure fair comparison. For Waymo and other local experiments, all baselines are retrained and reproduced with ego-motion compensation under identical device settings for consistent evaluation. Training

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Table 1: Performance comparisons on Argoverse 2 test set from the public leaderboard M. Upper groups are self supervised methods, lower are supervised methods. Our method achieves state-of- the-art performance in scene flow estimation. '#F' denotes the number of input frames. Runtime is reported per sequence (around 157 frames), with '-" indicating unreported runtime. 's', 'm', and "h' represent seconds, minutes, and hours, respectively. Purple highlighted runtimes indicate offline methods. Bold and underline mark the best and second-bes bost results.
Runtime per seq
Dynamic
Normal-Normalized 4
Three-way
EPE (em) J
Methods
#F
Mcan
CAR
OTHER
PED
VRU
Mean
FD
FS
BS
Ego Motion Flow
1.000
1.000
1.000
1.000
1.000
18.13
53.35
1.03
0.00
SeFlow 45
2
7.2s
0.309
0.214
0.291
0.464
0.265
4.86
12.14
1.84
0.60
ICP Flow 24
2
0.331
0.195
0.331
0.435
0.363
6.50
13.69
3.32
2.50
ZeroFlow 34
5.4s
0,439
0.238
0.258
0.808
0.452
4.94
11.77
1.74
1.31
FastNSF 22
12m
0.383
0.296
0.413
0.500
0.322
11.18
16.34
8.14
9.07
NSFP 21
2
1.0h
0,422
0.251
0.331
0.722
0.383
6.06
11.58
3.16
3.44
Floxels R3
13
24m
0.154
0.112
0.213
0.195
0.097
4.73
10.30
3.65
0.24
FalerFlow
35
all
24h
0.130
0.093
0.141
0.195
0.093
4.23
4.98
2,45
5.25
FastFlow3D
15
2
5.4s
0.532
0.243
0.391
0.982
0.514
6.20
15.64
2.45
0.49
TrackFlow 16
0.269
0.182
0.305
0.358
0.230
4.73
10.30
3.65
0.24
DeFlow 44
2
7.2s
0.276
0.113
0.228
0.496
0.266
3,43
7.32
2.51
0.46
SSF
17
5.2s
0.181
0.099
0.162
0.292
0.169
2.73
5.72
1.76
0.72
2
12.8s
0.174
0.095
0.167
0.278
0.155
2.51
5.73
1.48
0.30
Flow4D 18
15s
0.145
0.087
0.150
0.216
0.127
2.24
4.94
1.31
0.47
2
7.6s
0.145
0.084
0.144
0.225
0.125
2.30
4.81
1.44
0.66
AFlow (Ours)
5
8s
0.113
0.077
0.129
0.149
0.096
2.11
4.33
1.37
0.64
Table 2: Comparisons on Waymo validation set where each sequence contains around 200 frames. Upper groups are self-supervised methods, lower are supervised methods.
Foint Feature Extraction
Tontine per fromo (ms)
80
Trmppeal A Scheme
Backbome
Total
58.0
60-
Methods
Runtim
Three-way EPE (cm) 1
44.9
per seq
Mean
FD
FS
BS
40
SeFlow
45
14.8s
5.98
15.06
1.81
1.06
ZeroFlow
34
12.4s
8.52
21.62
1.53
2.41
NSFP 21
10.05
17.12
10.81
2.21
10
16
FastFlow3D 15
12.4s
7.84
19.54
2.46
1.52
Runtime breakdown of AFlow Argoverse 2 validation set
Figure 4:
DeFlow 45
14.8s
4.46
9.80
2.59
0.98
Flow4D 18
33s
2.03
4.82
0.78
0.49
as the number of input frames varies from to 15 (x-axis).
AFlow (Ours)
1.64
4.04
0.29
0.58
resources and settings are detailed in Appendix A.2
The code is open-sourced at httttss://gthhus
com/ htt//KinnWhange De tall ow along with trained model weights.
5 Results and Discussion
5.1
State-of-the-art Comparison
The Argoverse leaderboard test set results are summarized in Table 1 The proposed AFlow achieves the best mean EPE and dynamic bucket-normalized EPE scores among all methods, demonstrating both high accuracy and efficiency. It reduces mean dynamic bucket-normalized EPE by 13% compared to the second-best method, EulerFlow, and by 22% compared to Flow4D, while running twice as fast as Flow4D and thousands of times faster than EulerFlow. Even with two frames, AFlow outperforms all methods using the same setting, indicating that the A scheme effectively encodes motion differences between frames without subtracting out the important information. This of the-art art performance is consistently validated on other large-scale datasets. On the Waymo dataset (shown in Table 2). AFlow again achieves the lowest mean EPE, outperforming the next-best model Flow4D by 19% while being 45% faster. On the nuScenes validation set (shown in Table 3), AFlow establishes a new benchmark by significant margin, reducing the mean EPE by 39% compared to Flow4D. This consistently leading performance across datasets with different LiDAR configurations highlights the robustness and generalization capability of our approach.
7

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Table 3: Comparisons on nuScenes validation set with 10Hz LiDAR frequency, where each sequence contains around 200 frames. Upper groups are self- methods, lower are supervised methods.
Runtime per seq
Dynamic Bucket-Normalized I
Three-way EPE (cm)
Methods
#F
Mean
CAR
OTHER
PED
VRU
Mean
FD
BS
Ego Motion Flow
1.000
1.000
1.000
1.000
1.000
12.34
35.94
1.07
0.00
SeFlow 45
2
6s
0.544
0.396
0.635
0.726
0.419
8.19
16.15
3.97
4.45
FastNSF 22
2
2.6m
0.560
0.436
0.523
0.737
0.543
12.16
18.20
6.11
12.18
NSFP 21
2
3.5m
0.602
0.463
0,456
0.829
0.662
10.79
20.26
4.88
7.23
DeFlow 44
6s
0.314
0.163
0.286
0.533
0.275
3.98
6.99
3.45
1.50
Flow4D
9s
0.279
0.204
0.312
0.379
0.222
3.82
8.05
1.82
1.58
AFlow (Ours)
7s
0.216
0.138
0.219
0.327
0.181
2.33
4.83
1.37
0.79
Table 4: Scalability comparison of multi-frame scene flow estimation on the Argoverse 2 validation set. "#F" denotes the number of input frames processed. Flow4D and our AFlow are evaluated across increasing frame counts, reporting relative training speed, memory usage, and bucket-normalized accuracy.
0.000
FloudD
0199
0.155
10
0:101
0.100
00
10215
Dynamic Bucket-Normalizea
Method
Speed
Memory
Mcan
CAR
OTHER
PED
VRU
(1.10
1.03x
1.20x
0.2269
0.1648
0.1738
0.2960
0.2729
0,250
0.65x
x.85x
0.2147
0.1631
0.1767
0.2522
0.2667
Flow4D
0.37
2.82x
0,2022
0.1494
0.1707
0,2284
0.2603
0.17
0.21
0.26x
3.7x
0.2055
0.1593
0.1738
0,2280
0,2607
Mean Demamic Baclos Nermalized 1
Figure 5: Ablation study of the
1,04x
0
0.2116
0.1543
0.1751
0,2723
0.2449
1.00x
1.00x
0,1901
0,1479
0.1723
0,2160
0.2243
decay factor À in AFlow, evalu-
AFlow
0.68x
1,2x
0.1901
0.1500
0.1853
0,2010
0.2241
ated with 5 and 10 input frame
0.51x
1.22x
0.1916
0.1911
0.20X1
0.2242
settings.
5.2 Multi-frame Analysis
To further evaluate AFlow in multi-frame settings, we analyze its efficiency, scalability, and perfor- mance as frames increase, comparing it to Flow4D [18]. We also assess the effect of the time decay factor X in the A scheme on multi-frame processing.
Efficency and scalability Table 4 compares the computational cost and accuracy of AFlow and Flow4D across different frame counts. As the number of input frames increases, Flow4D experiences sharp drop in speed and a significant rise in memory consumption. By 15 frames, it requires 3.7x contrast, more memory and runs at only 0.26x speed, making large-frame modeling impractical. AFlow scales more efficiently, with only 1.22x memory growth and twice the speed of Flow4D at higher frame counts. Notably, the slowdown of AFlow mainly stems from the point feature extraction for each additional frame, as shown in the runtime breakdown in Figure 4, while the temporal A scheme and backbone-decoded network add negligible cost. As a result, Floow enables multi-frame processing without excessive computational overhead. This efficiency also validates the scalability of the A scheme, where the A feature maintains a constant feature size across frames, preventing the feature expansion problem seen in prior methods. Additional analysis A scheme efficiency is provided in Appendix B.I
Beyond computational efficiency, both AFlow and Flow4D achieve lower mean dynamic normaleno EPE with 5 or 10 frames compared to only 2 frames in Table 4 indicating that frami- modeling improves performance. However, this improvement diminishes or declines at 15 frames. A likely reason is that long-ago frames become less informative for predicting current motion, and incorporating such outdated context may introduce noise. This highlights an open challenge in optimizing long-term terg-eemm temporal information usage in real-time to maximize scene flow performance.
Performance
Time decay factor We evaluate different decay factor values (in Eq. (3) for 5-frame and 10-frame settings and summarize the results in Figure to analyze their impact on multi-frame processing. Overall, applying a decay X < 1 consistently improves mean dynamic bucket-normalized performance over the non-decayed X baseline, it emphasizes recent frames and downweighting older ones.
8

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0.26 0.32 (4)
VRU
0,202
Oklorr. Pretettii
0022
Sped
Mesta Augle
FoweD:
PloedD + 3q. (OOm))
AFwaw (Gax)
Mon Car
1:88 (1.7
Comera View
Grund Truth
Flow4D
A.Fow (Ouns
190 (502%)
0.200
Figure Qualitative comparison on the Ar- goverse 2. The left column displays camera views for reference, while the right columns visualize scene flow predictions, where Hue en- codes direction and saturation represents mag- nitude. Our method, AFlow, produces more accurate and consistent flow estimates than the prior SOTA, Flow4D, particularly for small ob- jects. (Best viewed in color.)
0.17
0.22
Barket-Normniianl
Figure 7: Ablation on our proposed loss (Eq. (8) compared to the baseline (Eq. (5) for both Flow4D and Allow. Red percentages indicate relative error reduction compared to the baseline loss. Bucket- normalized error across dynamic categories shows consistent improvements, especially for smaller classes like pedestrians and vulnerable road users.
Notably, even without decay, AFlow surpasses Flow4D [8]. demonstrating the robustness of our approach, with temporal decay providing additional performance gains. Additional per-category results for different À are provided in AApeedixx B.2
5.3 Loss Analysis
To assess the impact of our proposed loss functions on AFlow, analyze its performance across different object categories. As shown in Table 1| we observe that AFlow significantly improves pedestrian and wheeled object accuracy, reducing pedestrian error by 23.6% compared the next- best competitor, FulerFlow, demonstrating its ability to better capture small dynamic instances. Additionally, qualitative comparisons in Figure 6 further show that AFlow produces more accurate motion vectors than Flow4D, particularly for small objects like pedestrians, with points of the same pedestrian exhibiting greater motion consistency. These improvements might come from the contribution of the Category-Balanced Balanced Loss and Instance Consistency Loss.
To validate this, compare proposed loss functions Eq. (8) with the baseline loss Eq. (5) evaluating both Flow4D and AFlow, as shown in Figuree The results demonstrate that our loss consistently improves bucket-normalized accuracy across all dynamic categories, particularly for underrepresented small objects. The improvements are observed across both models, with mean, pedestrian, and VRU errors reduced by approximately 10%, confirming the general effectiveness of our loss design. Furthermore, while improving dynamic bucketed cocketed-normalized performance, our loss preserves static scene information, three-way mean EPE scores remain stable. More results and ablation studies on each loss item are provided in Appendix B.3
Table 5: Cross-domain generalization measured by the three-way EPE (cm) metric. Each model is trained on one dataset (LiDAR number and channel in parentheses) and evaluated on another with different LiDAR channel. Lower EPE indicates better generalization. Our proposed AFlow achieves the best performance in both evaluations.
Three-way EPE (cm) 1
Methods
Argoverse 2 (2x32) + Waymo (64)
Waymo (64) + Argoverse (2x32)
Mean
FD
FS
Mean
FD
FS
BS
SeFlow
451
5.98
15.06
1.81
1.06
6.29
15.56
1.16
2.16
NSFP
10.05
17.12
10.81
2.21
6.81
13.28
3.43
3.71
DeFlow 44
4.47
11.39
1.51
0.51
4.50
10.74
2.01
0.75
Flow4D
18
3.33
8.31
0.92
0.75
4.01
9.56
1.74
0.74
FFlow (Ours)
3.12
7.91
0.77
0.67
3.24
7.12
1.57
1.02

---

5.4 Cross-domain Generalization
AFlow also demonstrates strong cross-domain generalization, performing well when trained one dataset (Argoverse or Waymo) and tested on the other, as shown in [Talle 9 This setting is particularly challenging due to differences in sensor channels, point density, and scene distribution. To evaluate the cross-domain capability of AFlow, we include self-supervised methods such as SeFlow and NSFP baselines, which are trained or optimized directly on the unlabeled target domain. AFlow achieves state-of-the-art performance compared to both the baselines and other supervised methods, with three-way EPE of approximately 3em and foreground dynamic EPE of around 7cm. This strong performance is consistent across different object categories. A detailed breakdown of the dynamic normalzze EPE per category is provided in Appendix B.4
5.5 Visualization of the A Feature
To understand the effectiveness of our A scheme, we visualize feature maps from the feature della single-frame features (2t, -2-1, 2222), and the final backbone output Muuyy shown in Figure Each map is rendered by selecting the most activated channel after max projection along the Z-axis. Compared single-frame features, Daeta focuses "what is changing" in the scene. Zoom-in views (i) and (ii) in Zdeha show trail-like activations on moving vehicles, confirming that the A feature effectively captures dynamic cues. View (iii) highlights static background noise, which largely suppressed in Mun This demonstrates that after passing through the backbone, motion cues are further refined while irrelevant static context is filtered out. These visualizations confirm that the A scheme guides the model to attend to dynamic regions, enabling cleaner and more robust motion representations.
Single Frame
Feature Intensity
High
delta
9
Figure 8: Visualization of feature maps. Top: BEV projections; bottom: zoomed-in views. The first column shows the BEV map the point cloud Pt, while the remaining columns visualize normalized feature maps from Ddtta 2,, 2,-1, 1. 9-- by selecting the most activated channel after applying a max projection along the z-axis. Compared to the single-frame features, Ddela emphasizes regions with motion, such moving vehicles in panels (i) and (ii), while downplaying static structures like buildings in panel (iii), highlighting its motion-centric design. The final feature, (ou)). shows that the network further refines these cues.
and the final backbone output 2 (mm))- Each map is rendered
6 Conclusion
This paper introduces AFlow, an efficient framework for multi-frame scene flow estimation. addresses the scalability challenge by leveraging A scheme to extract motion cues without feature expansion as the number of frames grows. AFlow achieves state-of-the-ar performance on the Argoverse 2 and Waymo datasets while maintaining low computational cost and strong cross-domain generalization. Additionally, the proposed Gategory-Balaneee Loss and Instance Consistency Loss enhance learning for underrepresented small objects and enforce coherent object-level motion. With its accuracy and efficiency, Fllow is well-suited for real-world autonomous driving applications.
Limitations and Future Work While AFlow offers a highly efficient multi-frame pipeline for scene flow estimation, it currently relies on ground-truth annotations for supervised training. A promising direction for future work is to incorporate self-supervised learning strategies into the AFlow framework. This could enable high-efficiency, multi-frame scene flow estimation without labeled data, and enhance the real- time capabilities of self-supervised methods.
10

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Acknowledgement We thank Chenhan Jiang and Yunqi Miao for helpful discussions during revision. This work was partially supported by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. This work was also part financially supported by Digital Futures. The computations were enabled by the supercomputing resource Berzelius provided by National Supercomputer Centre at Linköping University and the Knut and Alice Wallenberg Foundation, Sweden.
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A Implementation Details
A.1 Method
Temporal A Scheme The A scheme in the sparse implementation, shown in Algorithm leverages
CUDA memory coalescing and bank conflict avoidance techniques for optimal efficiency.
Algorithm A Scheme Implementation
Notation: / (V. F) includes active voxel coordinate V and corresponding feature vector F. op E {0, @]
1: function SPARSEDELTA 2 A, LB. op)
2: (Vu, Fu) - sort_ batt_bby__ee by_key([V) Vnl: [A; Fp:
3: VA, Fx reduce_bbybyuyee byenye__ Fu)
4:
(VA, FA)
5: return 9
6: end function
Equation 3 Implementation:
7: Ddelta (0, 0)
Initialize with empty set b N: #Input frame
8: for + 1 No do
9:
// @: frame differencing
10:
Drop f- SPARSEDELTA (1, 2r-in +)
// (B: motion cue fusion
12: Ddelta < SPARSEDELTTA delta, X Prap: #
end for
Bockbone-Decodee Network We implement the 3D backbone MinkowskiNet18 network architec- ture in Backbone(-). using the spconv library following the design in Fig. 4 of [9]. The detailed implementation of Decoder(-) is described below, following 44
Z. (Convia (H,,1,, Fr-i]. W:))
R. (Convia (H,-1,, W,)
H. tanh (Convia id (R,: H F.-1, Wx))
H. Z, @ H + (1 Z.) H.
A MLP(H,FF,H) F,-1).
where H represents the previous hidden state at the i-th iteration. In the first iteration, H, is initialized using V2P (onn)) RVCC > R, 1xC as described in the main paper. The tensors Z. H. and F all have dimensions N where N is the number points and C/ the feature dimension. W., W,,, and W,, are trainable weight parameters in the convolutional gated recurrent unit (GRU). H is the final output of GRU.
A.2 Training Settings
39 test results directly obtained from the public leaderboard [1] to ensure a fair comparison. In the public leaderboard setting, evaluation is conducted within 70 70 m area (or 35 perception range) around the ego vehicle. To align with this, AFlow is initially trained on a 76.8 x 76.8 m grid, corresponding to a 38.4 m perception range. The voxel grid size 512 512 32 with voxel resolution our best-performing configuration. The number of input frames is set to 5, with time decay factor 0.4. The model is trained using the Adam optimizer (27), with batch size of 20 across 10 NVIDIA 3080 GPUs for around 18 hours over 21 epochs. We use cosine decay learning rate schedule with linear warmup. The learning rate reaches target of 10 after the 2-epoch warmup phase and then decays to minimum of 2 x 10-4
For leaderboard experiments, Argoverse
(0.15, 0.15, 0.15) in
For Waymo and other local experiments, all baselines retrained and reproduced under the same device settings to ensure consistent evaluation. To match default settings in prior methods, all models,
httpp: ptttps://github.ccom http://ghw....ceetet/eeeeee/////
14

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including ours, are trained with a voxel resolution of 0.2 m, spatial range of 51.2 m, fixed total of 15 epochs, and the same training augmentation on the same computing cluster. We used a batch size of 32, a fixed learning rate of 4 x 10-3, and trained on four NVIDIA A100 GPUs for all models. Runtime evaluations are conducted on a desktop system equipped with an Intel 17-12700KF processor and single NVIDIA RTX 3090 GPU.
For all experiments, to improve robustness against elevation variations and sensor viewpoint changes, we apply random height augmentation with 80% probability (uniform offset E [0.5, 2.0 along z-axis) and random flipping along the zy-axis with 20% probability per iteration during all training.
For loss formulations. we assign category weights we = [1.0, 1.5, 2.0, 2.5] corresponding to the mata-categories
[cars, other vehicles, pedestrians, VRUs] as defined by Argoverse 2 [3)]. We also apply speed-dependent weights % = [0.1, 0.5] for static (r- < 0.4m/s), slow-moving (0.4 Σ < 1.0m/s), and dynamic (v 1.0m/s) objects. These weights experimentally determined with focus on safety prioritization. Higher values are assigned to vulnerable road users (VRUs) and pedestrians to reflect their critical safety importance, well as dynamic objects. In the future, the weighting scheme within the loss function may be guided by multi-task learning strategy, such as the one proposed in 32 42
B Additional Analysis
Table 6: Comparison of the average number of voxels in Deeita across different frame set- tings (Sparse vs. Dense Representation) in Argoverse 2 validation set. The storage ratio is #Active Voxels
B.1 A Scheme Efficiency Analysis
Based on Brent's theorem [4], the parallel time com- plexity for the sparse A scheme in Algorithm I is 1ogVa1 + log" ((Val), where [VAl rep- Ny
calculated as #Dense Voxels x 100%. The dense baseline assumes resolution of XxYxZ= = 512 112x512x333 x32
resents the number of voxels containing points, and Np denotes the number of parallel threads. In multi- frame settings, while the number of active voxels [VA] increases with more frames, its growth rate re- mains low relative to the dense format, as reflected in the ratio shown in Tabll 6. Consequently, the time consumption for the sparse A scheme exhibits minimal variation across different frame settings in Fig. 3 of the main paper, consistent with our parallel time complexity analysis. In comparison with the dense matrix operation, which requires a parallel time complexity of 2([Vanee) the sparse operation achieves up to a 10x speedup and 100x memory reduction. This stems from the substantial disparity in the number of voxels to be processed, where V> >>>>> Vaense| as in Table 6
Frame
#Active Voxels
Storage Ratio
29475
0.35%
45310
0.54%
10
63745
0.76%
15
78666
0.94%
Dense
8388608
100.00%
Np
B.2 Temporal Decay Analysis
To integrate motion cues across multiple frames, introduce decay factor À in the A scheme, which progressively downweights older frames. [Table 7 compares in detail scene flow estimation performance on different À values for both 5-frame and 10-frame settings.
As shown in Table 7, incorporating consistently improves performance compared to the non- decayed setting (A=T). Notably, all decay configurations outperform the previous state-of-the-arr method, Flow4D, demonstrating the effectiveness our approach regardless of the specific À choice.
Different À values impact performance in distinct ways. A smaller À (e.g., 0.4) reduces errors for fast-moving objects (e.g., cars), while larger (e.g.. 0.8) improves static background estimation (Mean Three-way EPE). This suggests that lower À downweights older frames, benefiting fast motion, whereas a higher preserves historical context, enhancing stability in static regions. Further analysis on optimal À selection based on scenario dynamics will be explored in future work.
B.3 Loss Function
Table 8 compares different combinations of different loss items: motion-based Lastow 44 category- balanced, and instance-consistency, evaluated using Dynamic Buckkt-Norrallin metrics and three- way EPE.
15

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Table 7: Ablation study the time decay factor À in AFlow, evaluated on the Argoverse 2 validation set with 5 and 10 input frames.
Dynamic
Backet-Normalized
Three-war way
(em) :
#f
A/ Method
Mean
CAR
OTHER
PED
WHE
Mean
FD
FS
BS
0.2
0.1905
0.1488
0.1725
0.2163
0.2244
3.31
7.85
1.35
0.74
0.4
0.1901
0.1479
0.1723
0.2160
0.2243
3.31
7.85
1.35
0.74
0.6
0.1926
0.1501
0.1670
0.2182
0.2352
3.30
7.88
1.31
0.72
0.8
0.1915
0.1482
0.1750
0.2137
0.2291
3.26
7.84
1.24
0.70
0.2024
0.1493
0.1876
0.2268
0.2460
3.34
7.98
1.31
0.74
Flow4D [88
0.2147
0.1631
0.1767
0.2522
0.2667
3.59
8.49
1.39
0.89
0.2
0.1917
0.1537
0.1846
0.2070
0.2217
3.35
8.02
1,25
0.78
0.4
0.1901
0.1500
0.1853
0.2010
0.2241
3.30
7.94
1.23
0.73
0.6
0.1913
0.1514
0,1873
0.2021
0.2245
3.36
8.06
1.25
0.76
10
0.8
0.1954
0.1557
0.1789
0.2001
0.2471
3.26
7.84
1.24
0.70
0.1967
0.1505
0.1847
0.2087
0.2431
3.37
8.14
1.24
0.72
Flow4D [18
0.2022
0.1494
0.1707
0.2284
0.2603
3.45
8.09
1.46
0.81
Table Ablation study of proposed loss items. Results are evaluated on the Argoverse 2 validation set using the AFlow model (A = 0.8) with 5 input frames. Bold indicates the best performance, underline marks the second-bess and red highlights settings with significant performance drop.
Loss item category
Dynamic CAR
Three-way waye-wway EPE (cm)
Lacton
instance
Mean
OTHER
PED
VRU
Mcan
FD
FS
BS
0.2094
0.1504
0.1854
0.2398
0.2618
3.32
8.04
1.25
0.66
V
0.1962
0.1511
0.1732
0.2148
0.2457
3.27
7.94
1.22
0.65
0.1971
0.1501
0.1675
0.2238
0,2471
3.38
7.94
1.45
0.75
7
0.1881
0.1482
0.1609
0.2151
0.2280
3.93
7.84
1.27
2.69
4
0.1915
0.1482
0.1750
0.2137
0,2291
3.26
7.84
1.24
0.70
The baseline model includes only the motion-based loss 44 results. Adding the sategory-balancinn loss significantly improves performance for underrepresented categories, reducing pedestrian error from 0.240 to 0.215 and VRU error from 0.262 to 0.246. This stems from the increasing weight of these objects the gategory-balancing loss. However, increasing the weight of these categories slightly lowers accuracy for larger objects, such as cars. Despite this trade-off, the overall mean bucket-normalized error improves from 0.209 to 0.19..
which already achieves promising
Incorporating the Instance Consistency Loss improves performance across all dynamic objects, reducing the mean dynamic bucket-normalized error from 0.209 to 0.197 by enforcing consistency across moving instances. However, this comes with slight increase in three-way EPE, mainly on static points.
When using only the category-balances and instance consistency losses without motion--asel super- vision, the mean dynamic However, the three-way EPE increases sharply from 3.26 to 3.93 cm, mainly due to a spike in background static error (from 0.70 to 2.69 em). This highlights the importance of notion-based supervision in constraining overall scene flow predictions.
error drops 0.188 the best among all combinations.
The best balance between mean Dynamic Bucket-Normalized and Three-way EPE is achieved when all three items are combined. The mean Dynamic Bucket-Normalized error reaches 0.192, and pedestrian error decreases by approximately 1 11% compared to the motion-only bascline (0.240 to 0.214). Importantly, the three-way EPE remains stable or slightly improves (3.26 vs. 3.32 cm), showing that our full loss formulation enhances learning for smaller, dynamic objects without compromising motion estimation for the rest of the scene. These results validate the effectiveness of final loss design in improving accuracy.
B.4 Cross-domain Generalization
This section provides detailed per-category breakdown of the cross-domain generalization results discussed in Section 5.4 As shown in Table 9 the evaluation is conducted using the Dynamic Bucket-
16

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Normalized EPE metric. The results confirm that AFlow maintains state-of ofte--o-tthearr generalization performance across diverse object categories, such CAR. PED, and VRU, in both cross-domain settings. Notably, the largest gains are observed in the pedestrian and VRU categories, where motion and sensor-domain differences are the most significant.
Table 9: Detailed cross-domain generalization results using the Dynamic Bucket-Normalized HPE metric (lower better). Performance shown for Argoverse (2x32-channell) - Waymo (64- channel) and vice versa. The 'OTHER' vehicle category is not labeled in the Waymo dataset and is therefore excluded from the Waymo evaluation. Our method consistently outperforms competitors across all object categories in both cross-domain scenarios.
Dynamic Bucket-Normalized 4
Methods
Argoverse 2 (2x32) + Waymo (64)
Waymo (64) + Argoverse 2 (2x32)
Mean
CAR
PED
VRU
Mean
CAR
OTHER
PED
VRU
SeFlow
0.423
0.252
0.626
0.391
0.400
0.269
0.349
0.559
0.421
NSPP
0.574
0.315
0.823
0.584
0.597
0.427
0.319
0.915
0.728
DeFlow
0.346
0.156
0.545
0.339
0.326
0.201
0.267
0.434
0.400
Flow4D
0.217
0.091
0.424
0.135
0.205
0.158
0.195
0.218
0.246
AFlow (Ours)
0.198
0.091
0.395
0.109
0.194
0.155
0.184
0.203
0.234
B.5
Qualitative Results
The qualitative results in the main paper are derived from the scenes 'bbd62533-2232-33955-- 7fd8 1166c887 and -dfc32933-1524-3340 440.:-/2222444441155222221222222 we present additional qualitative results, comparing ground truth, the previous state-of-the method Flow4D [18), and our approach AFlow.
in the Argoverse 2 validation set. Here,
Eror (cm)
0.0
Scane
7.5
15.0
Scane
30.0
Camera View
Flow4D (#F=5)
A Flow (#F=2)
A Flow (#F 5))
Figure 9: Error maps comparison of 3D flow prediction from the Argoverse validation set, focusing on small objects such as pedestrians. The color bar represents the pointwise L2 norm error in centimeters. AFlow with '#F=2' denotes a two-frame input, while others use five frames. The two scenes correspond to scene IDs (eee77eee-992a-22224444669 94fe-fbcf39888411 and 198711ft4-b88e344 9161-ed961e7| la6d''..
Figure and Figure 10 illustrate enror maps for small (pedestrians) and large (trucks) objects, respec- tively. In Figure 9 the upper row (Scene 1) shows that AFlow with two frames improves motion consistency for pedestrians compared to Flow4D, highlighting the effectiveness of the Instance Consistency Loss. The bottom row (Scene 2) further demonstrates improved detection of under- represented small objects, suggesting that sategory-Balancee Loss enhances motion estimation for these classes. Figure evaluates large objects. AFlow better captures truck motion, demonstrating improved accuracy for large-scale dynamics.
Across all settings, five-frame AFlow outperforms the two-frame variant. This suggests that AFlow effectively captures global motion cues across multi-frames while maintaining stable input size.
The color-flow visualization in Figure 11 further supports these findings. Color shifts from the ground-truth color indicate discrepancies speed and direction. AFlow consistently outperforms
17

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Ener (cm)
0.0
Some
12.5
25.0
Soone 2
31,5
50.0
Camera View
FlowiD (#F=5)
Flow (#F=2)
Flow (#F=5)
Figure 10: Error maps comparison of 3D flow prediction from the Argoverse 2 validation set, focusing on large vehieles, such as trucks. The color bar represents the pointwise L2 norm error centimeters. AFlow with ##F=2' denotes a two-frame input, while all others use five frames. The two scenes correspond scene IDs "2c652f9e- -dd8
8db8-ddb8777 ------572--20 aa49-faf fae 1344a875b' and 1-004--300bbbb
Speed
Motion Angle (2D)
Ground Truth
FlowAD (#F=5)
Flow (#F-2)
4 (xF=5)
Figure 11:
Color-flow visualization comparison of 3D flow prediction from the Argoverse validation set. Direction is encoded as hue, and magnitude as saturation. Ground-truth labels are shown on the left. The three scenes correspond scene IDs '77574006-833 381f-3bc8-bbb6 11d79c002d83'. 778f7cb5c-9d5 111.3340033--3388--5533
and
Flow4D across static backgrounds (row 1), small objects (row 2), and large objects (row 3), with five frames yielding the most accurate motion estimates.
C Other Discussion
Broader Impact Our AFlow framework offers scalable and efficient multi-frame 3D motion estima- tion, enhancing safety and reliability in applications such as autonomous driving, robotic assistance, and augmented reality through improved dynamic scene understanding. Its scalability and compu- tational efficiency reduce overall resource consumption, contributing to more sustainable machine learning system development. However, the same efficient motion tracking capabilities could be misused for pervasive surveillance or unauthorized monitoring, posing privacy risks. Responsible data governance, strict access control, and adherence ethical deployment standards are essential to ensure the technology is used for societal benefit.
18

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25


Reviews:
[{"review_id": "YtcKUDMGcT", "reviewer": "Reviewer_jQn2", "summary": "This paper proposes a novel method for fusing temporal features from a 3D voxel grid into one representation that can be used for scene flow estimation. Rather than fusing features by concatenating along the channel or temporal axis, DeltaFlow instead proposes using \"delta features\" which represent the difference in the features over time. This allows for a compact feature representation whose dimension doesn't scale linearly with the number of timesteps aggregated. In addition, in order to address imbalances in the dataset, two new loss terms are introduced; a category balanced loss, and an instance consistency loss.\n\nThe delta features are computed by taking the sum of N differences between the current frame and the past N frames. Previous frames are then weighted by a temporal-decay factor ($\\lambda$) in order to bias the model to the most recent observations.\n\nCategory based loss upweights the loss on certain points based on their class, which allows classes with fewer points in the dataset (such as pedestrians) have better flow estimates. Additionally, the instance loss assigns an instance to each point and ensures that flow is consistent across the instance.", "questions": "## Questions\nMy main question is about the intuition of the delta feature scheme. Intuitively I understand what is being proposed, and empirically it clearly works, but the visualizations in Figure 7 don't quite line up with the intuition. There are clearly static areas which have high intensity features (likely because of differing scan patterns) and the more frames which are aggregated, the higher intensity these areas will be (because they are do not move). However the moving objects have a very distinct trail, and only exhibit high intensity features in the overlapping regions. So does this mean that if an object is moving very quickly with no overlap the feature intensity could be lower than a static region?\n\nOverall I think this figure could use some increased exposition.\n\n## Minor suggestions:\nVery minor nitpick but in Table 4, Argoverse 2 is listed as having 32 beams for its LiDAR. This is inaccurate as the point clouds from both 32 beam lidars are concatenated together giving a total of 64 beams. The cross domain generalization point still stands as obviously the sensor and scan pattern is completely different from WOD.\n\nThe NSFP listing in table 4 is also a bit confusing. Since it's a runtime optimization method, it cannot be trained on one dataset and evaluated on the other. I am assuming it's listed to serve as a baseline but this should probably be clarified.", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "## Strengths\nThe main strength of DeltaFlow is the novel delta feature design which provides significant efficiency gains and propels DeltaFlow to the top of the AV2 supervised scene flow leaderboard. The ablation studies of the proposed improvements (both the delta features, and the additional loss terms) are thorough and compelling. And the visualizations provided in the appendix highlight the specific types of improvements provided by DeltaFlow over the previous supervised state of the art method (Flow4D).\n\n## Weaknesses\nThe cross-domain experiments are the weakest section of the paper. The metrics provided are underwhelming (why only report 3-way EPE when both bucket normalized and 3-way are reported everywhere else?). Similarly in other section 5.3, stable 3-way EPE numbers are used to demonstrate a preservation of static performance, but really mean 3-way EPE also includes dynamic components, and the bucketed EPE metric includes a static component itself (which is identical to that of 3-way EPE). I think that this mixing of the metrics makes some of the results a bit confusing if one isn't as familiar with the various components of the metrics and definitely the presentation of these numbers could use some clean-up. It's not bad to have more metrics, but the clarity is affected in these sections.", "was_revised": true, "final_justification": "The authors have addressed my concerns in the rebuttal with additional metrics on the cross domain evaluation, I maintain my rating of accept.", "rebuttal": "Thanks for the valuable comments! We have addressed your concerns and questions individually below.\n\n---\n\n**W1: Dynamic-Bucket metric for cross-domain evaluation (Tab. 4)**\n\nWe omitted the Dynamic-Bucket metrics from Table 4 due to space constraints, but we agree they are important for clarity and completeness. We have now included the full results in Table 4a&4b below using the same bucket partitioning as in our main evaluations. DeltaFlow continues to achieve strong cross-domain performance on both dynamic bucketed and three-way EPE. We will revise Section 5.3 accordingly to clarify the metric distinctions in the final version.\n\nTable 4a: Argovsere 2 (2x32-channel) → Waymo (64-channel)\n\n| Method           | Mean Dynamic-Bucket ↓   | CAR ↓    | PED. ↓   | WHEEL. ↓  | Mean EPE Three-way ↓ | FD  ↓   | FS ↓    | BS  ↓  |\n| :--------------- | :-----: | :-----: | :-----: | :-----: | :----: | :----: | :----: | :---: |\n| SeFlow           | 0\\.4230 | 0\\.2521 | 0\\.6259 | 0\\.3910 | 5\\.98  | 15\\.06 | 1\\.81  | 1\\.06 |\n| NSFP             | 0\\.5740 | 0\\.3152 | 0\\.8230 | 0\\.5838 | 10\\.05 | 17\\.12 | 10\\.81 | 2\\.21 |\n| DeFlow           | 0\\.3465 | 0\\.1558 | 0\\.5446 | 0\\.3390 | 4\\.47  | 11\\.39 | 1\\.51  | **0\\.51** |\n| Flow4D           | 0\\.2171 | 0\\.0915 | 0\\.4244 | 0\\.1354 | 3\\.33  | 8\\.31  | 0\\.92  | 0\\.75 |\n| DeltaFlow (Ours) | **0\\.1980** | **0\\.0905** | **0\\.3946** | **0\\.1089** | **3\\.12**  | **7\\.91**  | **0\\.77**  | 0\\.67 |\n\nTable 4b: Waymo (64-channel) → Argovsere 2 (2x32-channel)\n\n| Method           | Mean Dynamic-Bucket ↓   | CAR ↓    | OTHER. ↓ | PED.  ↓  | WHEEL. ↓ | Mean EPE Three-way ↓ | FD  ↓   | FS ↓    | BS  ↓  |\n| :--------------- | :-----: | :-----: | :-----: | :-----: | :-----: | :---: | :----: | :---: | :---: |\n| SeFlow           | 0\\.3996 | 0\\.2686 | 0\\.3489 | 0\\.5595 | 0\\.4214 | 6\\.29 | 15\\.56 | **1\\.16** | 2\\.16 |\n| NSFP             | 0\\.5973 | 0\\.4270 | 0\\.3192 | 0\\.9154 | 0\\.7277 | 6\\.81 | 13\\.28 | 3\\.43 | 3\\.71 |\n| DeFlow           | 0\\.3258 | 0\\.2010 | 0\\.2673 | 0\\.4343 | 0\\.4004 | 4\\.50 | 10\\.74 | 2\\.01 | 0\\.75 |\n| Flow4D           | 0\\.2045 | 0\\.1582 | 0\\.1953 | 0\\.2181 | 0\\.2464 | 4\\.01 | 9\\.56  | 1\\.74 | **0\\.74** |\n| DeltaFlow (Ours) | **0\\.1939** | **0\\.1545** | **0\\.1845** | **0\\.2030** | **0\\.2338** | **3\\.24** | **7\\.12**  | 1\\.57 | 1\\.02 |\n\n---\n\n**Q1: Delta Feature Visualization**\n\nPlease note that Figure 7 visualizes the feature before sending it into the 3D backbone. \nDue to the different scan patterns, the ∆ scheme captures both static object and moving object features. \nAfter being processed by the 3D backbone, the network learns to distinguish consistent motion patterns from spurious or static differences. \nThe resulting feature map ($\\mathscr{D}\\_{\\text{out}}$) shows coherent motion trails on dynamic objects and reduced activation in static areas. \nFor fast-moving objects with little overlap, the feature map exhibits a clear motion trail and has a higher activation than static areas. \nWe will include a $\\mathscr{D}\\_{\\text{out}}$ visualization in the final version for clarification.\n\n\n---\n\n**Q2 \\& Q3: Argoverse 2 LiDAR and NSFP Evaluation Setup**\n\nFor Argoverse 2, we will revise Table 4 to explicitly list the setup as “2×32-beam” to reflect the dual-LiDAR configuration more clearly.\n\nFor NSFP, we follow standard practice and run it directly on each target dataset without labels, since it's a test-time optimization method. We'll clarify this setup in the final version."}, {"review_id": "L5FnaKIHcv", "reviewer": "Reviewer_6KZt", "summary": "∆Flow introduces an innovative and efficient multi-frame scene flow estimation method that leverages a differential framework to address challenges in autonomous driving scenarios. By incorporating a ∆ scheme, Category-Balanced Loss, and Instance Consistency Loss, the method enhances dynamic object estimation and improves efficiency, achieving approximately 2× faster inference compared to existing methods, while maintaining high accuracy. Experimental results on the Argoverse 2 and Waymo datasets demonstrate superior performance, particularly in dynamic object estimation. However, further comparisons with a broader range of methods, detailed analysis of computational complexity, and validation on more diverse datasets such as KITTI or nuScenes would strengthen the paper’s claims and provide a more comprehensive evaluation of its generalization capabilities and practical applicability.", "questions": "The difference-based method proposed in the paper is highly efficient; however, it is sensitive to noise in real-world environments, especially under the influence of sensor noise, occlusion, or lighting variations. Has the performance of this method been thoroughly evaluated in noisy environments? Has the potential interference caused by noise in the difference computation, which could affect the accurate estimation of dynamic objects, been considered?\n\nWhile ∆Flow shows good generalization between Argoverse 2 and Waymo, have you tested its performance on other autonomous driving datasets, such as KITTI or nuScenes, which may have different sensor configurations and environmental conditions?\n\nAlthough the paper mentions that ∆Flow is faster in inference speed compared to other methods, it lacks a detailed quantitative analysis of inference time, memory usage, and computational resource requirements. When comparing with other methods, the paper mentions that the inference speed is faster, but does not provide specific runtime analysis.", "limitations": "The differential method mentioned in the paper achieves improved efficiency; however, in real-world environments, especially under the influence of sensor noise and other factors, the differential method may be affected by noise. This could lead to errors in the model's dynamic object scene flow estimation, particularly when input data is of low quality or has high noise. Therefore, improving the model's robustness in noisy environments remains a challenge.\n\nThe current experiments are mainly focused on the Argoverse 2 and Waymo datasets, which are primarily from urban environments and use similar sensor configurations. While the model has achieved good results on these datasets, it has not been fully validated whether it can maintain the same performance in more complex or diverse scenarios, such as rural roads, highways, and extreme weather conditions.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength: Clear Methodology: The paper presents a solid and well-explained methodology for efficient multi-frame scene flow estimation. The approach employs a novel ∆ scheme for temporal information processing, which allows the method to scale effectively without expanding feature size. This is a key advantage, especially in autonomous driving applications that often require real-time, large-scale data processing.\n\nThorough Experiments: The authors provide comprehensive experimental results across two widely recognized autonomous driving datasets—Argoverse 2 and Waymo. The experiments demonstrate that ∆Flow achieves state-of-the-art performance in terms of both accuracy and efficiency. This solid empirical validation enhances the credibility of the proposed method.\nClarity:Well-Structured Presentation: The paper is well-organized and easy to follow. Key concepts like the ∆ scheme, network architecture, and loss functions are explained in detail, with helpful visualizations (e.g., diagrams and charts) to support the narrative.\n\nWeaknesses:\nSensitivity to Noise:The differential method proposed in the paper improves computational efficiency, but in real-world environments, especially under the influence of sensor noise, occlusion, and other factors, the differential method may be affected by noise. This could lead to errors in dynamic object scene flow estimation, especially with low-quality or noisy input data. Therefore, the model's robustness in noisy environments needs further improvement and validation.\n\nLack of Computational Resource and Real-time Performance Analysis:Although the paper mentions that ∆Flow is faster in inference speed, it lacks a detailed quantitative analysis of computational complexity, memory usage, and computational resource requirements. For real-world deployment in autonomous driving systems, especially on resource-constrained devices, the model's real-time performance and resource consumption will directly impact its feasibility and application. A more detailed performance evaluation is needed in future work.\n\nDependence on Labeled Data:Currently, ∆Flow relies on supervised learning with labeled data for training, meaning it requires a large amount of annotated data to be effectively trained. In practical applications, obtaining high-quality labeled data is often costly, and the labeling process may contain errors. Additionally, the lack of self-supervised or unsupervised learning capabilities limits its application in scenarios where labeled data is unavailable.", "was_revised": true, "final_justification": "The authors have addressed my concerns in the rebuttal, I maintain my rating of weak accept.", "rebuttal": "Thanks for the valuable comments! We have addressed your concerns and questions individually below.\n\n**W1 & Q1 & L1: Sensitivity to Noise**\n\nLiDAR noise can be broadly categorized as either structured noise (e.g., consistent noise pattern across multiple frames) or unstructured noise (e.g., random sensor jitter). \n\nFor structured noise, our Δ scheme helps mitigate its impact, as consistent patterns across frames are reduced through the subtraction step, allowing the network to better focus on the underlying motion signals; For unstructured noise, our Δ scheme reinforces coherent motion signals. As a result, the signal-to-noise ratio remains stable. Accumulated motion signals tend to form distinct, directional trails, making them easier to distinguish from scattered noise, which the network learns to recognize during training.\n\nPlease note that a full noise ablation is beyond the current scope; all our experiments are conducted on real-world datasets (Argoverse 2, Waymo, and the newly added nuScenes), which naturally include sensor drift, dropouts, and occlusions, etc. ΔFlow achieves SOTA performance across these benchmarks, confirming its robustness in noisy environments.\n\n---\n\n**Q2 & L2: Dataset Diversity**\n\nWe selected Argoverse 2 and Waymo as primary benchmarks because they are currently the only public LiDAR datasets with official scene flow ground truth and leaderboards, enabling large-scale, fair evaluation. While both focus on urban traffic, they differ in sensor setups and scan patterns,  providing a meaningful basis for cross-domain generalization.\n\nIn response to your suggestion for broader validation, we have additionally evaluated ΔFlow on nuScenes (Table R1), which features a single 32-beam LiDAR and includes diverse lighting and weather conditions. All methods used the same training settings (see Appendix C.2) on the nuScene train set. ΔFlow outperforms Flow4D by ~14\\% in mean bucket-normalized EPE (0.3652 vs. 0.4233), and by 21\\% on foreground-dynamic EPE (13.79 → 11.17). This confirms ΔFlow's robustness across three datasets with different sensor specs and environments. We will include the nuScenes results in the final version, and release code to support future evaluation on broader domains.\n\nTable R1: Performance comparison on the nuScene validation set.\n\n| Method           | Mean Dynamic-Bucket ↓   | CAR ↓    | OTHER. ↓ | PED.  ↓  | WHEEL. ↓ | Mean EPE Three-way ↓ | FD  ↓   | FS ↓    | BS  ↓  |\n| :--------------- | :-----: | :-----: | :-----: | :-----: | :-----: | :---: | :----: | :---: | :---: |\n| SeFlow           | 0\\.6900 | 0\\.5914 | 0\\.8100 | 0\\.7658 | 0\\.5929 | 8\\.26 | 20\\.33 | 3\\.25 | 1\\.20 |\n| NSFP             | 0\\.6888 | 0\\.5800 | 0\\.5529 | 0\\.8730 | 0\\.7492 | 9\\.96 | 23\\.32 | 4\\.12 | 2\\.44 |\n| DeFlow           | 0\\.4412 | 0\\.3661 | 0\\.4170 | 0\\.5751 | 0\\.4065 | 5\\.47 | 12\\.98 | 3\\.00 | 0\\.43 |\n| Flow4D           | 0\\.4233 | 0\\.4014 | 0\\.4133 | 0\\.4842 | 0\\.3944 | 5\\.32 | 13\\.79 | 1\\.67 | 0\\.49 |\n| DeltaFlow (Ours) | **0\\.3652** | **0\\.3474** | **0\\.3347** | **0\\.4454** | **0\\.3333** | **4\\.18** | **11\\.17** | **1\\.23** | **0\\.14** |\n\n---\n\n**W2 & Q3: Computational resources and Real-time Performance Analysis**\n\nWe apologize if the computational resource analysis is not clear enough. \nIn the current version, the computational resource analysis spans across the paper:\n- Section 5.2 presents a detailed breakdown of efficiency as the number of input frames increases. \n- Table 3 compares training speed and memory usage with Flow4D, while Figure 3 shows a component-wise runtime analysis, indicating that the Δ scheme adds minimal overhead.\n- Appendix D.1 provides a theoretical complexity analysis and quantifies memory savings from our sparse design (Table 5). \n- Appendix C.2 reports our training setup (10× RTX 3080 GPUs, 18 hours) and inference speed on a single RTX 3090 GPU, confirming real-time capability.\n\nIn the final version, we will try to make it clearer.\n\n\n---\n\n**W3: Dependence on Labeled Data**\n\nWe acknowledge that our current experiments use full supervision and note this as a limitation (Lines 298–302). However, the core ΔFlow framework is modular and adaptable to other objectives, such as self-supervised learning.\n\nTo demonstrate compatibility with self-supervised learning, we replace the fully supervised loss with the losses proposed in SeFlow. The training result is shown in Table R2, which confirms that ΔFlow can operate effectively without labeled data and even improve existing SSL accuracy. \n\nTable R2: Self-supervised methods, performance evaluated on Argoverse 2 validation set.\n\n| Method           | Mean Dynamic-Bucket ↓   | CAR ↓    | OTHER. ↓ | PED.  ↓  | WHEEL. ↓ | Mean EPE Three-way ↓ | FD  ↓   | FS ↓    | BS  ↓  | Runtime per seq ↓ |\n| :--------------------------- | :---------: | :---------: | :---------: | :---------: | :---------: | :-------: | :--------: | :-------: | :-------: | :------: |\n| SeFlow                       | 0\\.3996     | 0\\.2686     | 0\\.3489     | 0\\.5595     | 0\\.4214     | 6\\.29     | 15\\.56     | **1\\.16** | 2\\.16     | 7\\.2s           |\n| NSFP                         | 0\\.5973     | 0\\.4270     | 0\\.3192     | 0\\.9154     | 0\\.7277     | 6\\.81     | 13\\.28     | 3\\.43     | 3\\.71     | 1h              |\n| DeltaFlow  + SeFlow SSL Loss | **0\\.3346** | **0\\.2578** | **0\\.3042** | **0\\.4080** | **0\\.3683** | **5\\.17** | **13\\.03** | 1\\.50     | **0\\.97** | 8s              |"}, {"review_id": "4KHAr4VzNv", "reviewer": "Reviewer_iVVD", "summary": "This paper introduces ∆Flow, a lightweight 3D framework for efficient multi-frame scene flow estimation.  The key component of ∆Flow is the Δ scheme that captures temporal motion cues by computing differences between voxelized frames, maintaining computational efficiency regardless of the number of frames. Additionally, ∆Flow introduces a Category-Balanced Loss to handle class imbalance and an Instance Consistency Loss to enforce coherent motion for individual objects. Experiments show that ∆Flow achieves state-of-the-art performance with lower error and faster inference speed, and strong cross-domain generalization across the existing multi-frame supervised methods.", "questions": "- Can the authors provide more real-world arbitrary video inference results to better demonstrate the performance?\n- In Table 3,  the authors argued that \"long-ago frames become less informative for predicting current motion\". Is this related to the specific data distribution? When the average motion between frames is different, the amount of information contained in certain time intervals will be different. It seems that the amount of data used for training and evaluation is still relatively limited.", "limitations": "Please refer to Weaknesses.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n- This paper proposes the Δ scheme, which maintains computational efficiency regardless of the number of frames compared to previous multi-frame methods.\n- This paper introduces the Category-Balanced Loss and Instance Consistency Loss, which tackle the critical imbalanced object class distributions and motion inconsistency within objects in scene flow estimation. Ablation study also demonstrates the effectiveness of these two loss functions.\n- The paper is clearly written, and the experiments are adequate.\n\nWeaknesses\n- The main limitation acknowledged by the authors lies in ΔFlow's dependence on ground-truth annotations for supervised training, which would cause a domain gap in real-world settings, while obtaining accurate scene flow annotations is both challenging and expensive.\n- Although Δflow can efficiently process multiple frames, the maximum total number of frames for a single input is still only 15 frames, which is too low for real videos with high frame rates.", "was_revised": true, "final_justification": "The authors' responses regarding the reliance on ground truth annotation and the choice of specific window size are reasonable and address my concerns. I keep my score as accept.", "rebuttal": "Thanks for the valuable comments! We have addressed your concerns and questions individually below.\n\n---\n\n**W1: Ground Truth Annotation**\n\nWe acknowledge that our current experiments use full supervision and note this as a limitation (Lines 298–302). However, the core ΔFlow framework is modular and adaptable to other objectives, such as self-supervised learning.\n\nTo demonstrate compatibility with self-supervised learning, we replace the fully supervised loss with the losses proposed in SeFlow. The training result is shown in Table R2, which confirms that ΔFlow can operate effectively without labeled data and even improve existing SSL accuracy. Specifically, this ΔFlow-SSL variant reduced mean bucket-normalized EPE from 0.3996→0.3346 (\\~16\\%) and 3-way EPE from 6.29→5.17 cm (~18\\%) compared with SeFlow, while running at 8s per sequence, orders of magnitude faster than optimization-based NSFP (\\~1h).\n\nTable R2: Self-supervised methods, performance evaluated on Argoverse 2 validation set.\n\n| Method           | Mean Dynamic-Bucket ↓   | CAR ↓    | OTHER. ↓ | PED.  ↓  | WHEEL. ↓ | Mean EPE Three-way ↓ | FD  ↓   | FS ↓    | BS  ↓  | Runtime per seq ↓ |\n| :--------------------------- | :---------: | :---------: | :---------: | :---------: | :---------: | :-------: | :--------: | :-------: | :-------: | :------: |\n| SeFlow                       | 0\\.3996     | 0\\.2686     | 0\\.3489     | 0\\.5595     | 0\\.4214     | 6\\.29     | 15\\.56     | **1\\.16** | 2\\.16     | 7\\.2s           |\n| NSFP                         | 0\\.5973     | 0\\.4270     | 0\\.3192     | 0\\.9154     | 0\\.7277     | 6\\.81     | 13\\.28     | 3\\.43     | 3\\.71     | 1h              |\n| DeltaFlow  + SeFlow SSL Loss | **0\\.3346** | **0\\.2578** | **0\\.3042** | **0\\.4080** | **0\\.3683** | **5\\.17** | **13\\.03** | 1\\.50     | **0\\.97** | 8s              |\n\n---\n\n**W2 & Q2: Single input still 15 frames**\n\nWhile our current experiments use a 15-frame window, this is not an architectural limit. As shown in Table 3, performance saturates empirically around 10 frames, and we found limited additional benefit beyond 15. Therefore, this design choice reflects a research finding, not a technical constraint.\n\nArchitecturally, ΔFlow is fully scalable. As detailed in Appendix D.1, our sparse Δ scheme implementation ensures that even at 15 frames, active Δ voxels occupy less than 1\\% of a dense grid. This enables the processing of longer sequences. Compared to prior work (e.g., Flow4D), ΔFlow handles longer temporal windows more efficiently.\n\nAlthough our findings suggest diminishing returns beyond 15 frames, we note that this already represents one of the longest aggregation windows among current real-time methods. Given the 10 FPS rate of the datasets used, 15 frames span approximately 1.5 seconds, which is generally sufficient to capture relevant motion dynamics. For example, in scenarios where a vehicle transitions from steady movement to a sharp turn, earlier frames may contribute less to predicting current motion.\n\nThis observation is also consistent with prior work. For instance, Floxels reports optimal performance with 9–13 frames, and methods like Flow4D and MambaFlow are similarly evaluated on shorter windows.\n\n---\n\n**Q1: More Video Performance**\n\nDue to NeurIPS rebuttal guidelines, we are unable to include figures at this stage. However, we have provided qualitative results in Fig. 5, Fig. 9, Fig. 10, and Fig. 11 to illustrate real-world performance. In the final version, we will include a public project page with additional inference videos to allow readers to further assess ΔFlow’s behavior across diverse scenarios."}, {"review_id": "fDJdmLPUoF", "reviewer": "Reviewer_gKv8", "summary": "This paper introduces DeltaFlow, a novel and efficient motion representation. DeltaFlow models short-term motion as a delta between adjacent feature flows, which can be integrated into a recurrent encoder-predictor-decoder framework. The authors claim that DeltaFlow provides better motion cues while reducing computational cost and memory footprint. Experiments on standard benchmarks including Moving MNIST, KTH, Human3.6M, and KITTI demonstrate that DeltaFlow achieves competitive or improved prediction performance compared to existing motion representations such as optical flow and f-AR, with fewer parameters and faster inference.", "questions": "please refer to weaknesses.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "$\\textbf{Strengths}$\n\n1. DeltaFlow encodes motion as the difference between successive feature flows, which leads to a more compact representation compared to optical flow and f-AR, with reduced model size and faster runtime.\n\n2. The proposed method is evaluated on a wide range of datasets and shows consistent improvements in prediction accuracy and efficiency.\n\n3. The integration of DeltaFlow into a multi-stage recurrent architecture demonstrates good scalability and practical utility with fewer parameters and lower memory usage.\n\n$\\textbf{Weaknesses}$\n\n1. The paper should provide more detailed technical explanations on how the decay factor $\\lambda$ is set, as the relative importance of preceding and succeeding frames may vary across different scenarios.\n\n2. The experimental section does not include comparisons with recent state-of-the-art models such as Floxels, which limits the completeness of the evaluation.", "was_revised": true, "final_justification": "The authors have addressed all the concerns. I maintain my original score as borderline accept.", "rebuttal": "Thanks for the valuable comments! We have addressed your concerns and questions individually below.\n\n**W1: Decay Factor**\n\nWe apologize if the explanation regarding the decay factor was not sufficiently clear and are happy to summarize our findings here.\n\nAs shown in Figure 4 and Table 6, our Δ scheme already outperforms prior state-of-the-art (Flow4D) even with no decay applied (λ = 1). While applying a decay factor (λ < 1) yields modest but consistent improvements, the method is not highly sensitive to the specific value chosen, highlighting the robustness of the approach.\n\nFor this initial study, we adopted a simple fixed decay for clarity. We agree that learning λ dynamically based on scene characteristics is a promising direction for future work and can build on this foundation.\n\n---\n\n**W2: Comparison with Floxels**\n\nA comparison with Floxels is included in Table 1 (Page 7). As shown, ΔFlow achieves 26\\% lower dynamic bucket-normalized error (0.113 vs. 0.154), 42\\% lower three-way EPE, and is approximately 180× faster (8s vs. 24mins per sequence).\n\nGiven that Floxels is an offline optimization-based method rather than feed-forward, we focused our detailed comparisons on real-time supervised approaches such as Flow4D and DeFlow. We believe the Δ scheme could complement future multi-frame SSL pipelines like Floxels, and we see this as a promising direction for future work."}]

Author rebuttal:

Meta-review: The reviewers agree that this is a strong and novel contribution to multi-frame scene flow estimation. The core Δ scheme for temporal feature differencing is regarded as both original and efficient, enabling scalability to long sequences without linearly increasing feature dimension. The proposed category-balanced and instance consistency losses are also well-motivated and empirically effective. Extensive experiments on Argoverse 2 and Waymo, with added results on nuScenes, demonstrate clear state-of-the-art performance in both accuracy and efficiency.

Strengths shared across all reviews:
+ Novel delta feature design that reduces computation while improving accuracy (jQn2, iVVD, gKv8).
+ Thorough ablations and strong benchmarks, achieving SOTA with faster inference (jQn2, 6KZt, iVVD).
+ Clear and structured presentation of the method (6KZt, iVVD).
+ Demonstrated cross-domain generalization and potential adaptability to self-supervised setups (all reviewers after rebuttal).

Weaknesses raised:
- Limited clarity in cross-domain metrics and presentation of results (jQn2).
- Lack of detailed computational resource/runtime analysis and sensitivity to noise in real-world settings (6KZt).
- Dependence on supervised labels, raising concerns for practical deployment (6KZt, iVVD).
- Evaluation window capped at 15 frames, which may be restrictive for high-frame-rate video (iVVD).
- Missing details on decay factor setting and comparisons to all recent SOTA models (gKv8).

Rebuttal and Discussion:
The authors provided expanded cross-domain metrics, including dynamic-bucket evaluations, which addressed jQn2’s concerns. They clarified the Δ scheme’s behavior under noise and added experiments on nuScenes, strengthening claims of robustness (6KZt). They further demonstrated compatibility with self-supervised training, alleviating concerns on annotation dependence (6KZt, iVVD). The 15-frame window was clarified as an empirical choice rather than an architectural limit. Additional details were given on the decay factor and comparisons to Floxels (gKv8). Reviewers acknowledged these clarifications, with jQn2 and iVVD maintaining strong accept recommendations, while 6KZt and gKv8 held weak-accept/borderline scores but recognized that concerns had been adequately addressed.

Given the novelty, strong empirical performance, and convincing rebuttal that resolved reviewers’ main reservations, the AC recommends accept. This paper provides a clear advance in efficient multi-frame scene flow estimation and will be of broad interest to the vision and autonomous driving communities.
Decision: Accept (spotlight)