ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction
Authors: Jiabao Lei
Kewei Shi
Zhihao Liang
Kui Jia
Venue: NeurIPS 2025 poster ()
Keywords: 3d mesh generation
autoregressive modeling
coarse-to-fine
level of detail
Primary area: applications
TL;DR: Reversing mesh simplification into coarse-to-fine direct mesh generation with auto-regressive models.

Abstract: Directly generating 3D meshes, the default representation for 3D shapes in the graphics industry, using auto-regressive (AR) models has become popular these days, thanks to their sharpness, compactness in the generated results, and ability to represent various types of surfaces. However, AR mesh generative models typically construct meshes face by face in lexicographic order, which does not effectively capture the underlying geometry in a manner consistent with human perception. Inspired by 2D models that progressively refine images, such as the prevailing next-scale prediction AR models, we propose generating meshes auto-regressively in a progressive coarse-to-fine manner. Specifically, we view mesh simplification algorithms, which gradually merge mesh faces to build simpler meshes, as a natural fine-to-coarse process. Therefore, we generalize meshes to simplicial complexes and develop a transformer-based AR model to approximate the reverse process of simplification in the order of level of detail, constructing meshes initially from a single point and gradually adding geometric details through local remeshing, where the topology is not predefined and is alterable. Our experiments show that this novel progressive mesh generation approach not only provides intuitive control over generation quality and time consumption by early stopping the auto-regressive process but also enables applications such as mesh refinement and editing.

ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detal Prediction
Jiabao Lei'
Kewei Shi
Zhihao Liang,,
Kui Jia
1 The Chinese University of Hong Kong, Shenzhen
2 The University of Hong Kong
Tencent Hunyuan
https://jbles sitessttesssss sate/proj/aammssi
1%
5%
100%
Next-level-of-detail Prediction
0.1 %
0.3 %
5%
100%
Abstract
Directly generating 3D meshes, the default representation for 3D shapes in the graphics industry, using auto-regressive (AR) models has become popular these days, thanks their sharpness, compactness in the generated results, and ability represent various types of surfaces. However, AR mesh generative models typically construct meshes face by face in lexicographic order, which does not effectively capture the underlying geometry in a manner consistent with human perception. Inspired by 2D models that progressively refine images, such as the prevailing next-scale prediction AR models, we propose generating meshes auto-regressively in a progressive coarse-to-fine manner. Specifically, we view mesh simplification algorithms, which gradually merge mesh faces build simpler meshes, natural fine-to-coarse process. Therefore, we generalize meshes to simplicial complexes and develop transformer- based AR model to approximate the reverse process of simplification in the order of level of detail, constructing meshes initially from a single point and gradually adding geometric details through local remeshing, where the topology is not predefined and is alterable. Our experiments show that this novel progressive mesh generation approach not only provides intuitive control over generation quality and time consumption by early stopping the auto-regressive process but also enables applications such mesh refinement and editing.
Equal Contribution;
Corresponding Author: kuijia@cuhk.edu...
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
3D triangular surface mesh is the predominant representation in graphics. Due to its explicit control nature, compactness, and strong compatibility with modern graphics pipelines, it is important and has been widely used in various applications, such as the gaming industry and film production. Since 3D meshes are discrete and often non non-watertight, autoregressive (AR) models are increasingly popular for directly generating meshes instead of relying on intermediate representations like implicit fields, which may struggle with non-watertight, non-manifold, or thin-sheet surfaces. While AR models prove highly effective in modeling discrete ordered sequences in many other domains, such as natural languages, their application to meshes is less straightforward since mesh vertices and faces are inherently unordered. Prior works typically assign lexicographic orders (29] (for instance, from left
to right and bottom to top in canonical coordinate system) or face traversal orders [4] 48
60) to
transform a mesh into a ID sequence, and later employ an autoregressive model to learn the sequence directly for mesh generation. However, these artificially created orders are often less meaningful in geometry, failing to capture the overall shape during generation, and do not align well with how humans perceive objects in a hierarchical, coarse-to fine manner.
Such an issue also exists for AR models in 2D, where a raster scanning order for images is easy to implement but not optimal. Recent approaches, such as VAR [49, instead define the AR sequence as predicting the next scales, L.e. generating higher-resolution image from a lowor-resnlution one. We are therefore prompted to explore what the "next-scale" predictio for 3D meshes could be.
Unlike images or voxel grids that are structured regularly and allow for easy up- or down-sampling to obtain different resolutions, the "scale," more commonly known as level-of-detail (LOD) in graphics, is rarely explored for 3D meshes with deep learning due the irregular nature and complexity of explicitly managing a mesh's 's connectivity and topology. Nevertheless, one can still define the LOD for a mesh in terms of the number of faces or vertices. The widely accepted mesh simplification algorithms, such as QSlim [16], help by progressively reducing the face count of a mesh through the repeated collapsing of edges, where an edge connecting two vertices is merged into a single vertex. thus creating different levels of detail for the mesh. By leveraging a mesh simplification algorithm, we are motivated to train an AR model to learn from this reversed simplification sequence and generate meshes by progressively adding geometric details through local remeshing.
Our paper primarily draws upon two works [17 41 in the traditional area of mesh processing from several decades ago. Specifically, we propose an adapted version of (17), termed GSlim in this paper, which is designed to operate on and simplify simplicial complexes (introduced later in Oection(.11), a generalization of triangular meshes, within a unified framework. The algorithm is enhanced with the capability to allow for topological changes during simplification. With our algorithm, mesh, regardless of how complex its initial topology may be, will ultimately be reduced to a single point, benefiting from the use of simplicial complexes] which is unsupported by QSlim. The algorithm can provide information as byproduct on how we simplify a mesh in the LOD order. By reversing the simplification process, we can obtain a ID refinement sequence that progressively refines a mesh through local remeshing, an idea that has been roughly discussed by Popović and Hoppe [11]. The above algorithms essentially convert mesh into a 1D sequence. We then design tokenization scheme to discretize the ID sequence into compact tokens and subsequently train an autoregressive (AR) transformer using the tokenized sequences. This process can also be referred to as next- level-of-detail prediction, construct the next LOD. By employing our method, we can easily obtain a mesh with a user-specified LOD/complexity by early stopping the AR generation, which was unachievable in earlier work. Our experiments also show that such a trained transformer model is a useful and effective shape encoder that can faithfully capture shapes with high fidelity in the task of unconditional mesh generation.
the model essentially predicts refinement operations that add details to
In summary, to achieve direct mesh generation in the order of LODs, this paper proposes reversing the mesh simplification algorithm, thereby converting mesh into a coarse-to-fine fine mesh refinement sequence. We train an AR model on these sequences to predict the next L.Oss. During generation, the mesh initially starts from a single point and is iteratively refined according to the predictions made by the AR model, progressively adding geometric and topological details through local remeshing. Experiments show its streaming generation with flexible controllability over quality and time usage.
IIf we do not use simplicial complexes, an isolated single point cannot be described along with a triangular mesh. Additionally, simplicial complexes accommodate various types of meshes, including those with different topologies, watertight or non con-manifold cases, mixed dimensions, and on, indicated by [17.

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2 Related Work
Indirect Mesh Generation. A mesh can be indirectly obtained by converting it from other rep- resentations. Researchers have shifted their focus to studying generation with implicit fields after recognizing the ease of using these fields to handle different topologies 16 [4 39]. Numerous
studies 7 8 13 shapes purely geometrically. typically using signed distance fields 66 34 39], while others further explore how to encode both geometry and appearance within the same representation, typically employing neural radiance fields 20
25 26 27
28
39 43 have emerged along this line. Some aim to describe
36 [55]. Their representations can be either continu- post-procsssing step of iso-surface to convert their representation into a surface mesh. The drawbacks of indirectly generating meshes prompt to study direct mesh generation methods, as detailed below.
24
35
ous +
B5
36
39]
discrete 228 30 43 They often rely
extraction 31
Direct Mesh Generation. Initial attempts in this area involve deforming a shape template (c.g.. sphere) to a target [54 58], which is limited to fixed topology. Some approaches attempt to explicitly modify the topology [88] or leverage local surface patches to adapt the topology [8 19),
but still fail to produce a mesh with concise tessellation. Some methods capable of obtaining concise tessellation are based on intermediate representations and need to derive the mesh indirectly from them 88 [3]. PolyGen [37] is the first to directly generate mesh by explicitly generating its
vertices and faces. MeshGPT 45 learns codebooks to facilitate the encoding of triangular faces; some methods 3 4
21
60 strive to develop efficient tokenization strategies that convert 29
study the architecture for efficient training of mesh generation network. However, although there have been numerous works in this area, the paradigm they use mainly originates from (37). where the mesh is constructed face by face. In contrast, we attempt to generate mesh progressively in the order of levels of detail.
mesh into a one-dimensional sequence; some researchers 21 53
oorels-of-Detalll Representing signals with multiple resolutions can generally effective. Tradi- 16 22 42 focus on designing simplification algorithms that produce multiple levels from a given mesh input. Some works in deep learning [5] 36 40 (47) suggest producing im- plicit fields hierarchically however, they do not natively operate on the mesh itself. This is mainly due to the challenges associ- ated with handling mesh's connectivity. A recent work (48 in direct mesh generation attempted to incorporate an additional token for face count control; however, it does not intrinsically model different levels of detail, still essentially treating various levels as distinct meshes, A concurrent work named VertexRegen [61] is built upon progressive meshes [22), which require the initialization to be homeomorphic to the target mesh. However, our method does not have these restrictions.
tional methods [10
using hierarchical data structures to facilitate fin-grained representation;
Preliminaries
3.1 Generalizing Mesh into Simplical Complex
mesh can be considered exclusively composed of triangles. However, triangles alone are insufficient in this paper. Our method relies on a new representation called simplicial complex (SC), which a generalization of meshes. A simplicial complex further generalizes mesh to accom- modate (isolated) points and line segments that are not necessarily part of any triangles. Figure 2 illustrates this idea. We sometimes refer to an SC simply as a mesh in this paper for simplicity. Another benefit of using SC is its conciseness and abstractness in deseribing geometry. For example, line segments are better suited for describing skeletons, while an SC composed exclusively of points is essentially point cloud.
Figure 2: An simplicial complex example.
3.2 QSlim: The Standard Quadric- Baad Simplification Algorithm
To make our paper self-contained, we briefly introduce the widely accepted mesh simplification algorithm QSlim [16] here before formally introducing the GSlim algorithm that we actually used. For triangular face defined by the plane (x p) with |n|| = 1 and p being the barycenter, we can easily that the squared distance from point R to the plane n (x p) 0 can be calculated as:
(x(x) = (n T (x " T Ax + 2b 2b x
with A = A D=-Ap. c=pTAN Ap
3

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The above distance, also called the cost, is uniquely defined by the triplet Q. = (A, c), which is referred to as the fundamental quadric of We note that since geometric error can be measured in total as the sum of costs, the quadrie is essentially additive. The quadric of a vertex is therefore the sum of the quadries of all faces incident to that is, Q, = EOEN, Qo where N,, the set of faces incident to v. The quadric of an edge is defined as the sum of the quadries of its two endpoints, that is, Qe = Qu + uuy where ii and U2 are the two endpoints of e. If the edge e will collapse, will merge and 22 into a single vertex v" which is the minimizer of Qe. and the quadric of v* is updated with Q. = Qu + Quz. For simplicity, o* is practically determined by
v"
arg min (1 "
(e(
with the collapse cost being Qv()". This means the collapse position is taken from either the endpoints or the midpoint of the edge. We can calculate the collapsing costs for every edge in the mesh and employ greedy strategy to iteratively collapse the edge with the minimum cost found. A min-heap data structure will help find the minimum. The algorithm terminates when certain criteria are met, such as when the face count falls below the desired number. At the end of the algorithm, we will obtain a coarse mesh that homeomorphic (has the same topology) to the original mesh.
To preserve boundary edges, the algorithm needs to generate a perpendicular plane that runs through the edge. These constraint planes are later converted into quadries, weighted with large penalty, and added to the initial quadries for the endpoints of the edge. Apart from the inconvenience of preserving boundaries, there are also several limitations, including unchangeable topology and the inability to handle isolated points and edges. These limitations make the QSlim algorithm unusable for our task, since we envision that any mesh will eventually be simplified to a single vertex, which will require changes to both the topology and simplex dimension during simplification.
4 Method
4.1
GSlim: Generalized Mesh Simplification Algorithm
The GSlim algorithm we used addressed the aforementioned limitations (Section 3.2 It is adapted from [17] to enable topological changes. It is compatible with SC and supports reducing a mesh to the coarsest shape possible, which is a single point that also serves as the starting point for generation.
Unlike OSlim, which only defines fundamental quadrics for triangles, GSlim defines them for every simplex The quadric coefficient A for a simplex a of intrinsic dimension d is instead calculated as
A = Σí- e,e!
where {c:} } is its tangent orthonormal basis of and I is an identity matrix. larger quadric value in the above formulation will indicate that updates involving o are difficult, thereby postponing its edge collapse. Similarly, need aggregate nearby quadrics to compute the edge collapse quadric Qe. the calculation process of which has been detailed in Section [3.2] During the aggregation, we can optionally weight the fundamental quadrics with large penalty factor to adjust the strength of preserving that simplex. For example, if we assign a large penalty to the boundary edges, it will attempt preserve the boundary, which is much easier than QSlim. We have included an ablation study in Section 5.1 to investigate which set of penalty factors is the best.
It is interesting note that for mesh with n vertices, the algorithm requires n 1 steps to simplify it until only a single vertex remains, as each edge collapse reduces the vertex count by exactly one.
4.2 PSC: Reversing Simplification into Generation
Since the simplification process is many-to-one mapping, it is not inherently reversible unless additional information is recorded to specify how to reverse this process. The reverse operation of edge collapse is called "vertex split," and example is provided in Figure 4 By reversing simplification with vertex splits, one can reformulate a simplicial complex into a new representation called Progressive Simplicial Complex (PSC) 41 which consists of a starting point followed by sequence of vertex splits for coarse-to- fone refinement. Since in PSC only new simplices are added to the existing mesh with new indices, without altering the indices of pre-existing simplices, to convert an edge collapse sequence into a vertex split sequence, one must also reorder the simplices' indices so that they are in ascending order. The following information must be recorded for each vertex split:
A simplex may refer a point (d 0), edge (d 1). a triangle (d 2).

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Before the algorithm begins, we need to specify set of candidate vertex pairs for collapse. Unlike the convention [16] that uses candidate pairs from triangles, we further include "virtual edges" that bridge up disconnected components to facilitate topological changes. Figure 3 presents two examples of virtual edges for collapse. Following [41], these virtual edges are derived from the Delaunay tetrahedralization 57 of the input vertices. After the simplification applied, the algorithm will produce a sequence of increasingly coarsened meshes side products, visualized from right to left in Teaser the next section, we will discuss what information should be recorded during progressive simplification to facilitate our future use.
contraction
Figure 3: Two examples of gener- alized edge collapse. Two points will collapse into one point after contraction, leading to topologi- cal changes.
which vertex to split: integer index is sufficient for selecting the vertex for splitting
how the split is performed: boolean indicating whether the current position remains unchanged or becomes the midpoint of the split vertex pair
the relative positional offset: an offset vector for translating the new vertex position relative the current vertex position
how the topology changes adjacency: a list of topological labels for adjacent simplices
A vertex split operation can be represented as JSON configuration, which may look like:
"topo": [1, [1,2,5,3,3,4,6,7 The first three are quite straightforward, while the fourth is less intuitive, and we will elaborate on what it actually means and how derive it by explaining the example below.
{ "vsid":0, "midpoint" true, "offset": [1. 2.2.20..,233.
Table 1: Enumeration of topological cases.
Input
Output Cases After Vertex Split
Vertex Split
VO
Topological List
EO
E3
Ei
Ei
E2
Label
2
3
Index
Figure 4: An example of vertex split.
In Figure 4 a vertex split into two, resulting in the creation of new vertex Since the vertex split only influences its adjacent primitives (vertex 0 itself, five edges 0-4, and two faces 0,1)) the topological changes must occur solely in its adjacency. We can use a list called "topological list" to carry the topological change information for each adjacent simplices (always including vertex 0 itself), and its length is exactly the number adjacent primitives, as shown at the bottom of Figure 4 The list is first sorted by the dimension of the primitives, and then by ascending indices. Each entry in the list represents a classification label ranging from ~ 8, corresponding to the nine possible cases (VO, V1, EO, E1, E2, E3, FO, F1 and F2) summarized in Table
Let's interpret the topological cases in Table I For a single vertex marked as (source), it can either be split to form new vertex ti (target) create new edge st connecting s and t. They are respectively denoted as case and V1. Similarly, there are four cases for an edge: EO merely adds E; E1 switches the edge to connect with t; E2 creates a new edge to connect with t;; and finally, E3 creates a new triangle. The explanation for triangle cases analogous and omitted for brevity.
With Table I we can interpret the case presented in Figure 4 For instance, for edge il in Figure 4 after splitting vertex to create vertex 11, new face 2 is created, corresponding to case E3 in T We note that creating face 2 also implies that all its sub-simplices exist or are created as well, including edges 6, 5. and This also suggests constraint on the topological labels, i.e., case is inherently incompatible with E3, because the former suggests that edge st (specifically, the edge 5) exists, while the latter does not. There are many more hard constraints like this that the configuration must adhere to. The original paper 41) provides only incomplete rules and cannot be used directly for our purposes. We analyze and summarize all topological constraints into the following four rules:
5

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index
coordinate
vertex
face
edge
bit
id range: 0-255
256-511
512-513
514-516
517-520
521-522
Figure An example of tokenization layout for refinement operation.
1. If vo, then cannot have E3.
e C c1, f2 and e1, 2 C FO, then 61, f2 + E1.
3. If v C 62 and 61, 02 C F1, then 61, 62 + E0.
4. If v C 61, and e1, 62 C F2, then e,, e2 A EO and + E1.
A detailed explanation of rules (2-4) is provided in the footnote" These four rules complete and can be rigorously derived by thoroughly enumerating all possible cases a table and summarizing the rules that encompass each entry. They also indicate that we modify only the predictions of the edges to ensure that all the topological label predictions are consistent. We will leverage this property to design our tokenization layout, as shown in Figure [5] where the edge predictions follow the vertex and face predictions to facilitate the constrained decoding process introduced in Section 4.3
By formulating the vertex split operations (refinement sequence) as series of JSON configurations, we are able to progressively reconstruct a simplicial complex from a single point with the sequence. In the next section, we will detail how to turn this into learnable process with AR models.
4.3 Auto-Re Regressive Learning from Refinement Sequences
After obtaining the refinement sequences, we can utilize transformers to learn from these sequences We need to tokenize the sequence before feeding it into the transformer network. Unlike [56), which directly converts the structured input to textual format, we organize it in a compact layout. We show the operation layout after tokenization in Figure 55) In this example, there are three faces and four edges incident to the selected vertex, resulting in three squares colored in yellow and four squares colored in coral. We now explain the layout in detail: (1) The first two bytes encode the vertex index using int16, and each slot ranges from 0 to 255; (2) The subsequent six bytes encode the relative offset using fp16, with the first three bytes storing their most significant bytes, and each slot ranges from 256 to 511; (3) We then store the topological labels for the selected vertex, as well as incident faces and edges, respectively. There are only two cases for the selected vertex, so it ranges from 512 to 513. There are only three cases for the incident faces, so it ranges from 514 to 516. There are four cases for the incident edges, so it ranges from 517 to 520; (4) The last byte denotes a boolean indicating whether the current vertex is the midpoint after the vertex split. After all vertex split operations are tokenized, we should be able to obtain a long sequence by concatenating all tokens for autoregressive learning, Figure bbelow illustrates the network design for learning.
End
We simply adopt transformer network [52] to fit the se- quences. Since we primarily focus on unconditional gener- ation in this paper, the network receives input conditions. The network is responsible for predicting the next token un- til it reaches the end token and stops generation. However, predictions generated by the transformer may not always correspond a valid operation, analyzed in Section 4.2 We may need a solution to determine whether the predic- tion valid, possibly through constrained decoding, as shown below, to address this issue and ensure validity.
Autoregressive Transformer
Start
Operation
Operation
Operation
An example of autoregressive learning of three refinement operations.
Figure 6:
Apart from the four rules summarized in Section 4.2 there are additional constraints, such as those related to the vertex index and the relationships among different refinement configurations. To facilitate implementation, we can manually hardcode a function, denoted as ó(I; I1,..., 1;-1), that takes the newly generated token 2; input, conditioned on all the previous tokens {I1, ........ 2 and outputs a boolean value indicating whether the new token x; is compatible with the previous
"The second rule states that if there are two edges es and incident to the split vertex and are subset to a face with topological label of FO, then the topological labels of e and cannot be E1. The explanation for the other rules quite similar.
'We would like to note that our major contribution (Sections 4.1 and 4.2 is theoretically independent of how the learning scheme is designed; simply present the simplest learning solution here.

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CD w.r.. LODs
10
CD (x10-0
0.01%
10"4
10-3
10-7
10"
-F-356
#F-41,672
eF-2,035,189
Simplification
Figure 7: Mesh simplification results at different levels of detail. Our method incorporates isolated points and edges, which also help to approximate the original fine shapes. When simplifying 1%. the geometric accuracy remains nearly the same.
tokens ( (1 ). We hardcode the function e in Python with caching. The basic idea ensure validity is to use a depth-first search- tree traversal combined with random sampling to introduce diversity. The function d is evaluated each node, and the most probable node is selected for deeper traversal. If it cannot proceed further, it backtracks to the parent nodes to find alternative solutions. Using this constrained decoding strategy provides implementation guarantee that the operations predicted by the transformer are always consistent with the previously generated ones.
Experiments
Dataset. Our 3D mesh data mainly come from Stanford 3D Scans 50 Thingi10K 663, NeRF 35
AMASS [33, and ShapeNet (2). The ShapeNet data has been preprocessed by Siddiqui al. 45
which contains < 1, 700 vertices and < 800 faces for each mesh, and we follow their settings.
62 we adopt the following metrics for evaluation: Minimum Matching Distance (MMD), Coverage (COV), and 1-Nearest- -eiihhr Accuracy (1-NNA). For MMD, lower values better; for COV, higher values are better; and for 1-NNA, 50% is optimal. These metrics are calculated based on Chamfer Distance (CD). To measure visual similarity, we also use FID and KID scores assess visual quality, with lower values being better. We also report mesh compactness as the average number of vertices and faces per mesh.
Metrics. Following previous works 32 45
Implementation Details. For simplification, and faces to 0, 1, and 1, respectively, as their default values in our experiments. We follow the standard techniques in LLM, employing Byte Pair Encoding (BPE) to compress tokens. The entire vocabulary size 16,384, resulting in a length reduction of 2 ~ 3 times. We basically follow the setup of MeshGPT 45 for comparative experiments. We adopt 1 12-layer transformer with width of 768 for training, utilizing variable-lengle bf16 flash attention [T] for efficient training. The average batch size is z 60 per GPU. The learning rate is 10 4 for pre- pre-training across all categories and 10-5 for supervised fine-tuning on specific categories (chair, table, bench, and lamp). The model pretrained 4 H20 GPUs for 4 days and fine-tuned H20 GPUs for Rs 2 days.
set the penalty factors for vertices, boundary edges,
5.1 Ablation Studies
Simplification with Different Levels-of-detail, In this part, we study how the geometric recon- struction accuracy varies w.r.t. different LODs using our simplification algorithm. We test very complex LEGO shape from (35] that contains up to million faces. Visualization results, along with the numerical accuracy, are presented in Figure We find that our simplification algorithm indeed produces meshes with different LODs that consistently mimic the original shape.
Simplification on mon-manifold Meshes. We study the necessity of using proposed generalized simplification (GSlim) algorithm over the widely used QSlim [16] and present the results in Figure g Since QSlim cannot handle non-manifold cases, it either crashes during processing produces erroneous results. Our algorithm is often useful since many datasets contain non-manifold cases; using GSlim will enable direct processing of non-manifold mesh without preprocessing.
Simplification with Different Penalties. investigate how penalty factors affect the simplifica- tion results, we conduct experiments and present the visualizations in Figure We find that without the boundary edge penalty applied, the simplified mesh cannot maintain a hole in the middle, and the leg length is clearly shortened. With the vertex penalty applied, the resulting triangles become close
7

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#F-29,993 GSlim (Ours)
#F-29,998
#F=984 GSlim (Ours)
#F=1,000
QSlim
QSlim
Figure 8: Different mesh simplification algorithms. The popular QSlim algorithm may result in broken and cracked surfaces, while our algorithm (GSlim) still captures the overall shape perfectly, even when the mesh is non-manifold. The QSlim used is implemented by MeshLab [9].
equilateral; however, it cannot adaptively distribute its triangles to the geometric curvature. The best configuration is therefore VEF (0, 1,1, which is the default for all our other experiments.
GT
VEF=(0,0,1)
(EF=(0.1,1)
VEF=(1,1,1)
VEF=(1,0.0)
Figure 9: Different penalty factors used in simplification. The four right subfigures show the results with only 2% refinement steps applied. The notation "VEF" the bottom denotes the penalty values for vertices, boundary edges, and faces, respectively. It is clear that VEF = (0, 1, 1) is the best.
Training Accuracy Curve
1.0
0.8
warmup
0.6
0.4
0.2
0.0
5000
10000
Training Step
Figure 10: Mesh collection learning with 100 objects taken from the Thingi10K 63 dataset.
5.2
Direct Mesh Encoding
Direct Single Mesh Encoding Different Levels Detail. In this part, we study and compare methods capable of obtaining meshes with different resolutions in the context of single mesh fitting. From Figure [1 we find that our method can faithfully reconstruct the shape, while other methods, such DMesh 46 require significantly more training steps to achieve better results. Additionally, EdgeRunner 4X a pretrained model that receives point cloud as input, produces only three LODs and struggles to accurately reconstruct shapes higher LODs. These three LODs not only may correspond to poor quality and deviate significantly from the claimed number of generated faces but are also insufficient to meet practical requirements due the limited choices of LODs. In contrast, our method can produce any LODs as needed, and the number of generated vertices is precise.
Direct Mesh Collection Encoding with Transformer Networks. Following 44), we investigate
whether the refinement sequences can be effectively learned by the transformer using 100 objects. Although simple, the learning process could fail if the sequences are meaningless (nearly random) or local minima exist, which makes convergence unstable and slow. We present some fitted meshes from the Thingi 10K [3] dataset, along with the accuracy curve shown in Figure T0 Fortunately, we did not observe any of these obstacles during training. After the learning rate warms up (increasing
linearly to 10 40-4), we find that our method converges quickly to a very high accuracy, indicating its effectiveness in learning refinement sequences with transformer networks.
5.3 Unconditional Mesh Generation
We conducted unconditional generation experiments on four categories ShapeNet dataset. Visualization results presented in Figure 12 PolyGen 337 tends to produce simple and incomplete

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DMesh
Table 2: Quantitative results of unconditional mesh generation for two categories of the ShapeNet [2] dataset with different LOD ratios.
100
300
1000
8000
Edgeitunner
Training Step
Class
Rasio
covt
MMD
1-NNA
KID.
[V/][P]
1k
2k
4k
Face Count Conditioning
condition
GT
Lamp
0.5
0.2
65.45
71.79
2.05
1.54
51.74
63:21
27.91
10:44
0.0066
0.0013
109/
44/80
1.0
70.68
1.54
41.20
6.60
0.0005
216/418
Ours
41,07
86.53
0.0877
22/30
54.84
0.87
66.85
10.23
0.0022
105 196
Refinement Step
1.0
$6.29
0.75
39.81
2,63
0.0001
208 384
Figure 11: Different LOD methods in mesh reconstruction.
EdgeRunner [48] conditioned on point clouds.
Table 3: Quantitative results on unconditional genera- tion across four categories of the ShapeNet [2] dataset. Numerics are copied from 45
Method
MMD.
FIDI
KIDJ
BSPNa
01030
675/1166
Polveen
0.043
0.054
/7445
0,0001
198
AtlanNet
7.16
3.85
96.30
161.35
0.150
2500 4400
BSPNet
93.55
30.78
0.017
Table
Polygen
GLT3D
[5]
32.99
41.20
3.00
2.78
$5.54
$8.03
93.95
38.55
0.005
0.029
13767 27533)
147
GET
37.95
50.46
0.087
199 399
MeshGPT
45.68
2.36
72.85
6.24
0.002
90/
Oues
32.98
1.94
69.46
2,05
0,0002
156
AtlasNes 10
20.53
2.47
90.58
189
0.163
2500 40050
Banch
BSPNett
Polypen 15
51.92
28.74
2.05
1.97
76.98
$3.44
59.11
49.36
0.001
0.000
457 755
172 /430
PolyGen
MeshGPT
PivotMesh
Ours
MeshCPP
55.23
1.44
68.24
8.72
0.001
159 201
Ozzs
$6.29
0.75
39.81
2.63
0,0001
208 584
Figure 12: Visualization of unconditional direct mesh generation the ShapeNet 2 dataset.
AtlasNes
0.139
Tamp
Polyenn
8.025
0.077
185
387/1011
MrshGPT
3.94
65.73
19.9
0/004
150
meshes because requires separate training of the vertex and face models. MeshGPT 45 may generate meshes with messy tessellation due to its limited capabilities and learning challenges. PivotMesh [59] can produce plausible results, but some artifacts may be observed in local details. Our method successfully generates shapes with complex topology and clean tessellation. The numerical results in Table further validate the superiority of our approach in terms of generation diversity and fidelity, with most metrics surpassing those other mesh generation methods. Table 2 presents metrics for different simplification ratios. We find that 50% simplification still yields decent results. The average generation time (full) is ss minute, suggesting a potential additional speedup of 50%.
We also compare our tokenization scheme with other tokenization methods, such EdgeRunner 48 and BPT (60. in Table 4 under an unconditional setting. We observe that our method achieves comparable performance the other methods when all (100%) auto-regressive steps applied. Notably, we find that considerably superior when only few steps (10% 20%, 50%) are applied compared the other methods. This is because the intermediate results produced by scheme are consistently good approximations the finest level detail, whereas other approaches produce meshes in pertial-to-complle manner, causing their intermediate results to deviate significantly from the targets the generation process is not fully completed.
In the last two columns of Table we also present the average number of tokens required by each tokenization scheme, either per shape or per geometric element. We notice that our method, on average, needs fewer tokens to represent mesh than other methods, even though our method generally requires more tokens to represent a vertex than other methods do to represent triangle. This demonstrates the superiority of our tokenization scheme regarding compactness.

---

Table Quantitative results of various tokenization approaches 48 60
with different percentages
of auto-regressive steps applied are measured the bench category of the ShapeNet [2] dataset.
EdgeRunner 48
and BPT 66) are based on triangles, while the elements in our method are vertices.
COV
MMD
Token +
Methods
20%
50%
100%
10%
20%
50%
100%
per shape
per elem.
EdgeRunner BPT 60
48
9.43
30.99
40.33
54.90
10.32
4.87
2.59
0.81
5840
4.5
15.15
26.65
34.11
56.35
3.02
1.97
1.26
0.76
3235
2.73
Ours
41.07
47.40
54.84
56.29
1.67
1.15
0.87
0.75
2556
9.1
Course Input
Refined Oulput
Original Mesh
Edited Mesh
Edited Mesh
Figure 13: Our representation supports refining a coarse mesh input (top row) into fine-grained output mesh (bottom row).
Figure 14: A coarse skeleton can be easily derived using our approach for fine-graines mesh editing using surface deformation.
5.4 Possible Applications with Our Approach
Shape Refinement from Sketchy Inputs. Our method can also be used to refine 3D sketchy shape, as shown in Figure 13 This is practically useful for 3D modelers, as they only need to specify coarse outline without expending effort fine-grained geometric details, significantly saving time.
Shape Editing by Manipulating Coarse Skeleton. A skeleton can be easily derived using our approach to facilitate the manipulation of a fine shape, as shown in Figure 14] By modifying the coarse skeleton, marked in red, one can easily manipulate the human shape through surface deformation.
Limitation, Future Work and Conclusion
Like prior works 45 the main drawback of our method is its relatively limited generalization ability compared to those built upon continuous space (e.g., Diffusion). Using an order-of- order-of-mannitude larger amount of training data may alleviate this problem. To suppress excessive topological flexibility, may use PSC to create an initial result with the desired topology and then use the normal progressive meshes representation 22 for the remaining steps of further refinement without changing the topology. During generation, we may reduce the linear complexity to logarithmic complexity by using parallel vertex splits (14 23 in future work. Lastly, our method lacks gradients to update the PSC: therefore, would interesting to derive differentiable PSC that can adaptively fit a mesh in coarse-to-fin manner through local remeshing with gradient guidance.
This paper suggests formulating direct mesh generation the order of levels of detail (LOODs), consistent with how humans perceive objects, and generating in preferable coarse-to- manner. The basic idea is to generalize meshes to simplicial complexes, reverse the mesh simplification process, and train model to learn mesh generation, initially starting with a single point and iteratively refining previous coarse results. Experiments verify the promise and effectiveness of our approach.
Acknowledgment
sincerely thank Prof. Zhen Liu for valuable discussions regarding our work. This work was supported by the Key-Area Research and Development Program of Guangdong Province, China, under Grant 202480101040004 for the project titled "Research and Application of Common Key Technologies for Embodied Intelligence of Robots Based AI Large Models."
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Reviews:
[{"review_id": "yRivSIlZqL", "reviewer": "Reviewer_HBFZ", "summary": "This paper formulates the triangle mesh generation process as an autoregressive (AR) prediction on the next level-of-detail. The key idea is to ask the AR model to learn the mesh “densification” process (reverse of simplification) while the simplified results are provided by mesh simplification method geometry processing. The produced sequence naturally forms a sequence of increasing levels of detail. The challenge is to “translate” the full sequence of mesh densification to tokens that are compatible with the AR model. For that purpose, the paper proposes a generalized mesh simplification method and designs a method to serialize the vertex split operation as a token. With the train AR model, the resulting system is able to produce a realistic sequence of generation. The authors also show results of mesh simplification (with the proposed modified simplification method), mesh generation, fitting and application such as editing and guided generation given user input.", "questions": "1. “Virtual Edges” in (a bit after than) Line 136: I like the idea to include topological change.\n- (a) How are these virtual edges represented in the later tokenization process? The paragraph in Line 159-171 is great, walking the audience through the newly defined concepts. It would be great to describe other examples (in particular, corner case scenario) with some examples (maybe in the supp. mat.).\n- (b) While flexible, allowing topology changes can also open a box of worms, enabling the model to create a mesh with unacceptable topologies. Will the proposed system suffer from this? How to prevent it?\n\n\n2. I appreciate Section 4.2 as it tries to define the vertex split operation and formally “serialize” the operation as a symbol to be compatible with later AR model learning processes. The paper also explores properties of the topological constraints. Are the four rules in Line 180 complete? How to show if the rules here are complete.\n\n\n3. The example in Line 154 is not fully explored. The “topo” list: I see that those integers refer to the case ID in Table 1 (and Line 166). So those values in that example are not corresponding to the example in Fig 4? This part is a bit confusing. Currently I assume the content in Line 154 is just arbitrary and not connected to later paragraphs.\n\n\n4. It’s a missed opportunity to use the newly defined rules/topo case in Line 167-184 to explain the example in Fig. 4. The “Topological List” in Fig 4 is still not easy to understand.\n\n\n5. The fitting experiment in Fig 11: can the authors provide a more detailed description of how this experiment is done? What loss function/process to guide the generation towards the target bunny mesh? What starting point (single vertex, or a rough shape of the bunny mesh) for the generation? \n\n\n6. Any failure case examples? The limitation section in Line 292 mentioned the limited generalization issue. Can we see some examples? Will it have geometry artifacts and/or topology issues?", "limitations": "I’m concerned about the robustness of the method. Can it always produce nice geometry and topology? See my comment in Question section item 1 and 6.\n\n\nThe authors mentioned the generalization issue in the limitation section. Can we see some examples and do some analysis?", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\n- Very interesting formulation to convert the progressive generation process of triangle mesh into autoregressive sequence prediction. \n- The key element of the paper is how to convert progressive mesh generation (vertex split operation) into an AR model compatible token.\n\n\nWeakness:\n- I’m concerned about how robust the generated results are. In particular, will the mesh have topology issues since the model allows flexible change of topology.\n- The authors put quite some effort on explaining the tokenization process. But there are still quite some parts that are not very clear. This would be key to this paper, and it would be great to address my questions, as those might be the questions for future audiences.", "was_revised": true, "final_justification": "The rebuttal addressed my concerns. The method presents novel ideas, solid reasoning process and good results. I will improve my rating to \"acceptance\".", "rebuttal": "We are truly grateful to the reviewer for dedicating their valuable time to provide us with such constructive feedback. We sincerely appreciate your insights and will now address your questions, hoping that our responses will adequately address your concerns. In accordance with this year's rebuttal policy, we will provide a textual response only, without any external links. Thank you once again for your understanding and support.\n\n1. We are truly thankful to the reviewer for their kind appreciation. We wholeheartedly agree that introducing topological changes allows any chosen mesh to be simplified to a single point, serving as a universal starting point for generation. Your recognition of this point is deeply appreciated and means a great deal to us.\n\n   **(a) How are these virtual edges represented in the later tokenization process?** The presence of a (virtual) edge is encoded in the topological list, with the first element indicating whether the edge exists. Specifically, the case V0 in Table 1 signifies that the edge is virtual, while V1 indicates that the edge is real and will be present after the vertex split. The topological list is then tokenized into a sequence of classification tokens, as illustrated in Figure 5. We sincerely recognize that our explanation of these new concepts may not be fully sufficient, and we will provide additional clarifications and examples in the supplementary materials to enhance understanding. We truly appreciate your understanding and support.\n\n   **(b) Flexible topology changes.** Thank you for your insightful observation! We are grateful for the insights that guide us in this direction. At each vertex split step, we have the flexibility to modify the topology of neighboring simplices as needed. For instance, in the case of a mesh with 100 vertices, where each vertex has an average of 10 neighboring simplices, we estimate an upper bound of $10 \\times (100 - 1) = 990$ opportunities to modify the local topologies. It’s important to note that this is an upper bound, as the topological constraints outlined by the four rules will slightly reduce this number. This observation underscores the remarkable flexibility of our approach. However, we have observed some unacceptable changes when utilizing a poorly trained model with limited generalization ability. This has led to generated meshes that appear random and do not reflect typical shapes. To address this challenge, we believe that a straightforward yet effective solution is to ensure that the model is well-trained. Additionally, we have some ideas that may address this problem more comprehensively. For instance, we could allow the model to predict a coarse mesh with 10 vertex splits that introduce all the essential topological changes contributing to the overall topology, while the remaining 90 vertex splits would maintain the overall topology. In this scenario, our model would effectively reduce to a \"progressive mesh\" method (rather than a \"progressive simplicial complex\" method), introducing mesh subdivision without topological changes, thus enabling us to better control the complexity of these changes. We view this as an important direction for future work, and we appreciate your guidance in this matter.\n\n2. **Are the four rules in Line 180 complete?** We are truly grateful for your interest in these four rules! We humbly believe that these four rules are complete, serving as both sufficient and necessary conditions. We have carefully derived them by thoroughly enumerating all possible cases in tables and summarizing the rules that encompass each entry. For those who are interested, we would be glad to provide a rigorous proof in the supplementary material. In a broader sense, our proof can be viewed as somewhat analogous to deriving logical expressions from truth tables.\n\n3. **So those values in that example are not corresponding to the example in Fig 4?** The topological list $[1, 2, 5, 3, 3, 4, 6, 7]$ presented in line 154 corresponds to Figure 4. As indicated in lines 165~166, this list can be converted to: V1, E0, E3, E1, E1, E2, F0, F1, which describe the topological changes of the eight simplices in the left subfigure of Figure 4. For instance, vertex 0 is classified as V1 because a new edge 5 is created following the vertex split; face 1 is categorized as F1 because it was originally connected to vertex 0, but after the split, it connects to the new vertex. We also observe that the lengths of these two lists are equal, reflecting the number of star simplices, which includes vertex 0 itself along with its adjacent edges and faces. We appreciate your attention to these details!\n\n4. **It's a missed opportunity to use the newly defined rules/topo case in Line 167-184 to explain the example in Fig. 4.** We have provided explanations for the topological cases in Figure 4, along with examples in lines 172$\\sim$174, and we briefly discuss the reasons for the existence of these rules in lines 174$\\sim$178. However, we acknowledge that the few examples presented in the current paper may not be sufficient, and we intend to provide further clarifications. For the zero-dimensional simplex, we focus on the selected vertex 0. We observe that after the split, it creates an edge 01 that connects the original vertex 0 to the newly created vertex 1, which corresponds to the topological case V1 in Table 1. Additionally, for edge 3, which originally connects to vertex 0, after the split, it is no longer connected to vertex 0 but instead to vertex 1. This indicates a transition from the source vertex to the target vertex, representing the topological case E1. Similarly, face 1 falls under the topological case F1, as it is now incident to the new vertex 1, as shown in Table 1. Regarding the constraint rules discussed in lines 180~184, we will provide an example and focus on the second rule for further explanation. If there are two edges, e1 and e2, incident to the split vertex and they are subsets of a face with a topological label F0, then the topological labels of e1 and e2 cannot be E1. This is because a face labeled F0 implies that its sub-simplices (e1 and e2) must also be incident to the source vertex \\(s\\), which contradicts the case E1 where the edge is connected to the target vertex \\(t\\). We appreciate your patience and understanding, and we will elaborate further in the supplementary materials, including an additional video to illustrate this point more clearly. Thank you for your interest!\n\n5. **The fitting experiment in Fig 11: can the authors provide a more detailed description of how this experiment is done?** Let us provide some additional details regarding the experiments presented in Figure 11. DMesh is a differentiable Delaunay triangulation method that learns from a mesh input. We use the target mesh as input and allow DMesh to perform optimization, with its intermediate outputs reflecting its progressive learning outcomes.\nEdgeRunner, on the other hand, is a large-scale pretrained direct mesh generation network that takes a point cloud as input and produces a mesh in a predefined scanning order (not in a coarse-to-fine manner during the generation process). However, it offers only three levels of complexity conditioning, 1k, 2k, and 4k, without options for other complexities, such as 3k. Consequently, we utilize their method by feeding a point cloud as geometry conditioning and the complexity conditioning token (1k, 2k, or 4k) as input, resulting in a mesh output. \nWe would like to note that although it is claimed that a 4k conditioning should ideally produce a mesh with 4k faces, our observations indicate that the generated mesh contains approximately only 2k faces. This suggests that their method may not effectively control geometric complexity, even when provided with an additional face count (complexity) token as input.\nFinally, our approach is similar to that of DMesh, where we require the target mesh as input and learn the progressive generation process. The intermediate figures illustrate the progressive results during auto-regressive generation. As shown, our method can accurately control geometric complexity; the number below our subfigure, such as 256, indicates that the mesh has exactly $256 + 1 = 257$ vertices. The face count can be indirectly and less accurately influenced by the number of vertices. We utilize the method described in Section 4.3 to learn the generation process using cross-entropy loss, as we essentially perform token classification after tokenization. The generation process always begins with a single vertex. We sincerely appreciate your interest in our implementation details!\n\n6. **Any failure case examples?** Yes, we acknowledge that our method can sometimes yield unsatisfactory results, which we believe are primarily due to generalization issues. Unfortunately, due to this year's rebuttal policy, we are unable to include images here; instead, we would like to describe our findings.\nEach vertex split operation encodes both geometry (e.g., relative offset) and topology (e.g., the topological list), and we have observed that these failure cases reflect both aspects. Geometric artifacts may lead to local shifts; for instance, a chair's leg might be slightly offset by a translation vector of $(0.5, 0, 0)$ due to the discretization of the offset. While the overall topology remains unchanged, the leg is simply misplaced.\nTopological artifacts present more significant challenges. For example, a mesh may be generated correctly in the first 10 steps, but if an incorrect topology is predicted at the 11th step, this error can cause the result to deviate from the original intent, often resulting in an unrecognizable outcome as the shape falls out of distribution. We are committed to including a detailed analysis of these artifacts, complete with figure examples, in our revised paper. We sincerely appreciate your understanding and feedback as we work to improve our approach."}, {"review_id": "nWdcblG9ku", "reviewer": "Reviewer_KceG", "summary": "This paper proposes a novel autoregressive (AR) framework for 3D mesh generation that constructs meshes in a coarse-to-fine manner, departing from the conventional face-by-face generation paradigm. Inspired by next-scale prediction in 2D image generation, the authors model the mesh generation process as the reverse of a mesh simplification procedure. They leverage a transformer-based AR model to reconstruct the mesh, starting from a single vertex and gradually increasing geometric detail without a fixed mesh topology. The method improves mesh quality and supports downstream tasks such as mesh refinement and editing. The method is novel in the field of mesh generation as it's the first next-scale prediction mesh generation method.", "questions": "1. **Training and inference speed.**  \n   How does the training and inference speed of the proposed method compare with face-by-face generation methods such as MeshGPT?\n\n2. **Extension to conditional generation.**  \n   Can the proposed framework support conditional refinement or editing tasks, such as conditioning on an image or partial point cloud?\n\n3. **Failure rate.**  \n   What is the failure rate of the method during generation? Prior face-by-face methods often exhibit limited success when generating high-face-count meshes—how does this method compare?\n\n4.  Lack of comparison experiments with recent strong baselines and the absence of experiments on conditional generation.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n1. **Novelty.**  \n   The paper introduces a new perspective on mesh generation by reversing the mesh simplification process and formulating it as a progressive coarse-to-fine autoregressive task. To the best of our knowledge, this is the first work to adopt a next-scale prediction approach for meshes, analogous to recent advances in 2D generation.\n\n2. **Application.**  \n   The proposed coarse-to-fine generation process naturally enables applications such as mesh refinement and editing, which are challenging to achieve with conventional face-by-face generation schemes.\n\n3. **Clarity.**  \n   The paper is well-written and provides a thorough description of the proposed method.\n\n## Weaknesses\n\n1. **Limited comparison.**  \n   The paper lacks comprehensive comparison with other recent mesh generation methods such as MeshXL, MeshAnything, and DeepMesh, all of which are publicly available.\n\n2. **Lack of conditional generation.**  \n   The experiments are limited to unconditional generation. Given that applications like mesh refinement and editing naturally arise in conditional settings, it is important to validate the proposed method under such scenarios (e.g., conditioned on an image or point cloud).", "was_revised": true, "final_justification": "I maintain my positive rating.", "rebuttal": "We are sincerely grateful to the reviewer for generously dedicating their time to provide us with such constructive feedback. We are committed to addressing your questions in a manner that we hope will effectively resolve your concerns. In line with this year's rebuttal policy, we will provide a textual response only, without any external links. Thank you for your understanding and support.\n\n1. **Training and inference speed.** This aspect is indeed quite practical, and we appreciate the opportunity to discuss it. Both our method and MeshGPT utilize auto-regressive techniques, but the primary distinction lies in what determines the generation complexity: our approach is based on the number of vertices $V$, while MeshGPT depends on the number of faces $F$. Typically, for a mesh, there is an approximate relationship of $F \\approx 2V$, which suggests that our method may require fewer geometric elements for generation. In our experiments, when generating 100 meshes randomly and unconditionally, *our method generally takes about 60 seconds per shape, whereas MeshGPT averages around 80 seconds*. We would like to humbly emphasize that these speed metrics were obtained using a single H20 GPU. Regarding training speed, it largely depends on the computational resources available; generally, longer training times lead to better generalization. For our model, we typically require about 16 GPU-days, while MeshGPT necessitates a total of 24 GPU-days to complete its training. Lastly, we wish to acknowledge that actual performance may vary slightly across different platforms and machines. We appreciate your understanding in this matter.\n\n2. **Extension to conditional generation.** Thank you for highlighting the importance of conditional generation tasks! They are indeed invaluable for practical scenarios. We believe that our proposed framework has the potential to support additional tasks, such as conditional refinement, editing, or generation from images or point cloud inputs. To accommodate different modalities, we may consider established conventions that convert images or texts into tokens using ViT or BERT for feature extraction, subsequently fusing these features into our transformer via cross-attention mechanisms. \nWe must humbly acknowledge that achieving these tasks requires very large models and substantial amounts of data. Unfortunately, we are currently limited by our computational resources and time, making it challenging to train large-scale models on extensive datasets during the rebuttal period. We sincerely apologize for this limitation and remain committed to pursuing this direction by extending our methods to perform conditional generation tasks in the future. We sincerely appreciate your understanding and consideration. Thank you for your support.\n\n3. **Failure rate.** Thank you for highlighting the aspect we previously overlooked. Indeed, there are notable works in the related field aimed at supporting the generation of meshes with a high face count, such as Meshtron, which claims the ability to generate meshes with up to 10k faces, significantly more than what our current study addresses.\nIn our experiments, we found that the failure rate of our method is acceptable, remaining below 5% across 100 randomly generated objects. This metric was measured on the ShapeNet dataset, which includes shapes with fewer than 1,700 vertices and 800 faces each. We sincerely acknowledge that we currently lack the computational resources and time necessary to conduct large-scale experiments focused on generating high face counts. As such, we have positioned our paper to explore the potential advantages of using our progressive simplicial complex representation before scaling up to larger models or datasets. We appreciate your understanding in this matter.\nAdditionally, we have observed that using our trained model for extrapolation, specifically, performing additional refinement steps with training on a low face-count dataset, is not feasible. This limitation arises because our tokenization process includes the vertex index, which restricts our model's capabilities based on the vertex count. As a result, the model has not encountered cases with a high number of vertices, leading to poor generalization when applied to meshes with high face counts. We are grateful for your understanding of this limitation. We will certainly discuss this point in the limitation section of our revised paper.\nFinally, we would like to share a strategy for managing failure cases. We have observed that unsatisfactory results often become apparent within the first few generation steps. For instance, after generating just 10 steps, we can often determine whether the current generation will yield acceptable results. If the produced outputs show low confidence in generation (as indicated by the classification probability of the generated tokens), we can recognize a potential failure early and stop the generation process. Thank you once again for your valuable feedback.\n\n4. **Lack of comparison experiments with recent strong baselines and the absence of experiments on conditional generation.** We sincerely apologize for not including comparisons with recent strong baselines (such as publicly available methods like MeshXL, MeshAnything, and DeepMesh) on the tasks of conditional generation from texts, images, or point cloud inputs. We are committed to discussing and citing these methods, as well as presenting our limitations, in our revised paper. We must acknowledge that, due to limited computational resources and time, we are currently unable to perform these tasks, as they require training on a very large dataset and utilizing a large-scale model. Instead, we chose to focus on unconditional generation tasks, which our baseline method, MeshGPT, also addresses. Comparing our results with MeshGPT is more feasible for our experiments, given the lower resource requirements. Additionally, we positioned our paper to explore the benefits of using the newly developed progressively simplicial complex representation before scaling up to such large datasets and models. We genuinely hope for your understanding regarding this limitation and greatly appreciate your support."}, {"review_id": "Jd4L6siQog", "reviewer": "Reviewer_1KDk", "summary": "The paper proposes a novel method to generate meshes in a coarse-to-fine manner. To construct a compatible representation for arbitrary topology, especially the starting point, the authors generalize 3D meshes to simplicial complexes and adapt the commonly used mesh simplification algorithm to GSlim. By tokenizing the vertex split operation, the paper parses each mesh as a 1D refining sequence that can be further modeled with a transformer-based AR model.", "questions": "I am generally positive about the paper. The paper proposes a good way to model meshes in a coarse-to-fine way. But the tokenization process seems too complicated, making the sequence quite long. I think it's a big limitation on how far we can go. What do we get out of making such sacrifices, in other words, are there some potential solutions, or how can we utilize the intermediate results? What is the difference between generating the whole mesh and them simplifying it, and the proposed method?\n\nOther comments:\n- The title of section 3.1: simplical -> simplicial", "limitations": "Yes.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The method to tokenize the simplification operation is non-trivial and well-designed.\n- The overall writing is good, making the technical details clear.\n\nWeaknesses:\n- For a mesh with N vertices, the length of mesh sequences is roughly larger than $10N$ or even longer, which is longer than per-face per-coordinate tokenization. This may hinder the model ability to generate complex meshes.\n- Compared to direct mesh generation, it is not entirely clear how we can use the intermediate results for some potential applications. Although there are some mentions, no detailed algorithms or results are given in the article.\n- The dataset and evaluation are limited. At least, edgerunner, meshanything, BPT are quite relevant but they are not shown in the quantitative results. Shapenet is not diverse enough for mesh generation.", "was_revised": true, "final_justification": "The rebuttal addresses most of my concerns except the comparison against strong baselines (edgerunner, BPT). I will keep my original rating.", "rebuttal": "We are sincerely grateful to the reviewer for generously dedicating their time to provide us with such constructive feedback. We are committed to addressing your questions in a manner that we hope will effectively resolve your concerns. In line with this year's rebuttal policy, we will provide a textual response only, without any external links. Thank you for your understanding and support.\n\n1. **The tokenization process seems too complicated, making the sequence quite long.** Thank you for highlighting this limitation! We would like to clarify that our paper does not specifically focus on proposing an effective tokenization method; rather, we present a straightforward solution to make it work (as noted in footnote 4 at the bottom of page 6). In practice, we adapted techniques from LLMs to reduce the number of tokens, employing Byte Pair Encoding (BPE) for compression in our experiments. On average, this approach can reduce token lengths by approximately 2$\\sim$3 times. \nFor example, a mesh with 500 vertices and 1,000 faces (where $F \\approx 2V$) and an average tokenized length of 10 would require $ (500-1) \\times 10 = 4,990 $ tokens to represent a highly complex mesh. However, with BPE, this number can be significantly reduced to about 2k tokens. In comparison, a baseline method using per-face per-coordinate encoding would need $ 1,000 \\times 9 = 9,000 $ tokens, which can also be reduced to around 2k tokens using BPT [1]. \nIt is evident that the compression ratio of our method is comparable to recent strong compression baselines, which underscores a major benefit of using progressive representation for compression, as highlighted in [2]. We truly appreciate your understanding and support in this matter.\n\n\n2. **How can we utilize the intermediate results?** We appreciate your feedback on this aspect! One of the key advantages of our representation is the ability to obtain intermediate (coarse) results without needing to generate the mesh with the highest complexity. For instance, consider a simple case where our ground truth is a mesh with 500 vertices and 1,000 faces. Conventional methods may require a total of 1,000 steps for generation; if fewer than 1,000 steps are taken, the resulting mesh may appear incomplete, with some faces missing, making it less representative of the ground truth.\nIn contrast, our method allows us to obtain the ground truth mesh in just 499 steps. Moreover, in many cases, we do not require a mesh of such high complexity. For example, if we only need a simplified version, we can perform even fewer steps (e.g., 100 steps), and the resultant mesh will still closely resemble the original ground truth. By reformulating mesh generation in a coarse-to-fine manner, we can effectively control both geometric complexity and the time and computational budget required to generate a mesh with the desired complexity.\nFinally, the coarse mesh can be utilized in various scenarios, such as game development and streaming or previewing the generation process. We sincerely appreciate your concerns and support in this discussion.\n\n\n3. **What is the difference between generating the whole mesh and them simplifying it, and the proposed method?** We sincerely appreciate your attention to this point! It is indeed a fascinating aspect. The primary advantage of our approach is its ability to save both time and computational resources. When the network is trained with a high-fidelity mesh dataset, conventional methods often require an excessive number of generation steps to produce high-fidelity meshes, making the process quite costly. Additionally, an extra simplification process is needed if a low-poly result is desired. \nWhile one could train multiple models with varying mesh complexities to partially address this limitation, we believe this is not the ultimate solution. Our approach allows for greater control over the time and computational budget required for generation, enabling us to achieve results with fewer inference steps. We hope our method can make a positive contribution to our community, and we are truly grateful for your kind support and understanding.\n\n---\n\n[1] Haohan Weng, et al. Scaling Mesh Generation via Compressive Tokenization. CVPR 2025.\n\n[2] Hugues Hoppe. Progressive meshes. SIGGRAPH 1996."}, {"review_id": "LUkwWDcbWN", "reviewer": "Reviewer_L8JW", "summary": "This paper proposes ARMesh, a novel autoregressive framework for direct 3D mesh generation that synthesizes mesh progressively from coarse to fine levels of detail (LOD), departing from conventional lexicographic face-by-face generation. Its core contributions are:\n1. Insight:\nLimitations in current AR mesh generators (e.g., MeshGPT, PolyGen) lies in constructing meshes in fixed orders unrelated to geometric hierarchy. ARMesh models the generation porcess by next level-of-detail(LOD) prediction compure to next scale generation in 2D image generation problem, which able to model the unorder 3D space.\n2. Generalized Simplification (GSlim):\nIntroduces a topology-aware mesh simplification algorithm operating on simplicial complexes which generalizing meshes to include points/edges. It reduces any input mesh to a single point in n-1 steps, producing a fine-to-coarse LOD sequence.\n3. Progressive Simplicial Complex (PSC):\nReverses GSlim into a generative coarse-to-fine process which enables the following AR mesh generation process.\n4. Autoregressive Modeling:\n  - Tokenizes PSC sequences into discrete vocabularies.\n  - Trains a transformer decoder to predict next refinement tokens autoregressively.\n  - Employs constrained decoding (DFS + hardcoded rules) ensuring topological validity.", "questions": "1. Could the authors evaluate ARMesh on a large-scale 3D dataset (e.g., Objaverse, ShapeNet-XL) to assess scalability and generalization? I fully understand that full training might be infeasible during rebuttal period, minimal experiments (e.g., fine-tuning on a subset) or qualitative results would suffice.\n2. Could the authors compare ARMesh with SOTA autoregressive methods? I understand they are trained on some large-scale dataset like the objverse. Could author re-train them on identical dataset which paper use?\n3. Could authors provide quantitative results on condition generation result? For example: coarse mesh/sparse point cloud conditioned.", "limitations": "1. Scalability to Real-World Complexity： The training and evaluation of ARMesh is limited to small-scale datasets. Its performance remains unverified on large-scale, diverse 3D collections (e.g., Objaverse. Without validation on high-complexity shapes or diverse topologies , claims of generalizability remain speculative. This restricts confidence in real-world applicability.\n2. Unexplored Conditional Generation: While ARMesh intrinsically supports progressive refinement (Fig 13–14), its potential for conditional generation—e.g., text-guided LOD synthesis or point cloud completion—remains unexplored. The method’s coarse-to-fine paradigm is theoretically well-suited for such tasks (e.g., refining sketch inputs to detailed meshes).", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths\n1. Originality & Significance:\n  - Novel Next-LOD Prediction Paradigm: Proposes a fundamentally new autoregressive approach (Next-LOD prediction) for mesh generation. This departs significantly from prior lexicographic/traversal-order face-by-face generation, offering a more geometrically reasonable (coarse-to-fine) generation process. This is a conceptually original contribution to the field.\n  - GSlim & PSC Framework: Introduces the generalized simplification algorithm (GSlim) enabling topology changes and reduction to a single point, and its reversible counterpart (PSC). This technical innovation is crucial for constructing the LOD sequences and is a significant advancement over traditional simplification (e.g., QSlim) for generative modeling.\n2. Technically Sound Foundation:\n  - The core methodology (GSlim simplification → PSC reversal → tokenization → AR transformer training) is well-motivated, rigorously described (esp. topological constraints and tokenization), and demonstrates clear technical competence.\n3. Clarity:\n  - Well-Structured and Readable: The paper is exceptionally well-written. The problem motivation (limitations of prior AR orderings), inspiration (2D next-scale prediction), proposed solution (LOD reversal), and technical details (GSlim, PSC, tokenization) are presented logically and clearly. Figures effectively illustrate concepts (e.g., vertex split, topology cases).\n\n\nWeaknesses\n1. Limited Scalability Demonstration:\nTraining and evaluation are conducted primarily on small-scale dataset. Crucially, recent state-of-the-art methods (e.g., EdgeRunner, MeshXL) leverage large-scale datasets like Objaverse. This omission raises concerns about the method’s scalability and generalization capability to complex, diverse shape distributions.\n2. Incomplete State-of-the-Art Comparison:\nWhile comparisons against PolyGen and MeshGPT are provided, Table 3 lacks critical benchmarks:\n  - GET3D results for the Bench and Lamp categories\n  - Contemporary baselines (e.g., EdgeRunner, MeshXL, MeshAnything) that report strong unconditional generation performance.\nValidation against these methods on larger datasets (e.g., Objaverse) would significantly strengthen empirical claims.\n3. Insufficient Ablation Analysis:\nWhile ablation studies explore LOD ratios and penalty factors, key design choices lack rigorous validation:\n  - Impact of transformer architecture/configurations (depth, width, attention mechanisms)\n  - Tokenization alternatives beyond the proposed scheme\n  - Quantitative and qualitative ablation results would better elucidate the contribution of individual components.\n\n4. Narrow Scope in Conditional Generation:\nThe work focuses exclusively on unconditional generation. But it will be easy to adopt this method into condition mesh generation. Demonstrating efficacy in conditional settings (e.g., text-to-mesh, point cloud completion) would enhance the practical impact and versatility of the approach. Comparisons with conditional mesh generators are notably absent.\n\n**If the authors solve my concerns during the rebuttal, I will increase my score to 5.**", "was_revised": true, "final_justification": "The authors have solved my concerns, I will raise my score to 5.", "rebuttal": "We are profoundly grateful to the reviewer for generously dedicating their time to provide us with such invaluable feedback. **In summary, we have decided to reserve additional experiments (e.g., conditional generation on large-scale datasets) for future work.** We truly appreciate your understanding of our intentions. Your understanding and support mean a great deal to us, and we would like to elaborate further on this.\n\nWe wholeheartedly agree with the reviewer that providing additional experimental results on conditional generation (such as from images, texts, or point clouds) would significantly enhance the persuasiveness of our method’s effectiveness. However, we currently find ourselves constrained by limited computational resources and time, which regrettably prevents us from conducting these additional experiments that require large-scale training, as this process is indeed quite time-consuming and costly. We hope you can kindly understand our limitations.\n\nWe also sincerely appreciate the reviewer’s thoughtful suggestion regarding minimal experiments (e.g., fine-tuning on a subset). However, we humbly feel that fine-tuning networks from other methods may present challenges for a fair comparison, as those networks have been trained on significantly more data than a network trained from scratch with a smaller dataset. We are grateful for your understanding of our perspective on this issue.\n\nIn our current paper, we have conducted extensive ablation studies to explore the potential properties of our newly proposed representation, along with some unconditional generation results that serve as preliminary experiments demonstrating the efficacy of our progressive simplicial complex representation combined with deep learning for facilitating mesh generation in a coarse-to-fine manner. We humbly believe that scaling up to larger datasets and exploring diverse tasks can be effectively pursued in future studies. We sincerely appreciate your understanding, and we hope our work can still make a positive contribution to our community.\n\nThank you once again, and we wish you a wonderful day!"}]

Author rebuttal:

Meta-review: This paper receives 2x accepts and 2x borderline accepts. The reviewers think that the proposed method is novel, the paper is well-written with clarity,  and the proposed method is technically sound and solid. The paper also shows good experimental results. Although there are some concerns on limited comparisons with other methods in the experiment section, the reviewers think that this is a minor concern and accept the paper. The ACs follow the ratings of the reviewers to accept the paper.
Decision: Accept (poster)