Flow Matching Reinforcement for 3D Mesh Generation via Dynamic Homing Optimization

• Adapted RL objectives mainly repel velocity directions for negative trajectories without specifying a target velocity field, and yield limited 3D geometric gains under stated constraints.The stated constraints include pretrained-model capabilities, rollout diversity, and reward-distribution complexity.Source: §1 · p. 2
• DHO pairs each negative sample with a distinct positive target through batchwise minimum-cost matching, then constructs a remaining-time-aware corrective velocity toward that target.Source: §1 · p. 2
• Flow3D-Pro applies asynchronous online DHO to image-to-3D mesh generation; DHO updates forward-process interpolants from rollout endpoints and needs no full-trajectory storage.DHO is also sampler-flexible.Source: §1 · p. 2
• DHO outperforms representative DPO-, GRPO-, and NFT-style objectives in 3D generation, while Flow3D-Pro achieves higher geometry quality than current mesh-generation methods.Source: §1 · p. 2

2.1 3D MESH GENERATION

• Recent rectified-flow 3D systems mainly study pre-training, representation, or sampling, while DHO focuses on RL post-training for 3D geometry generators.Source: §2.1 · p. 3

2.2 REINFORCEMENT LEARNING FOR FLOW MATCHING

• Flow-matching RL objectives adapted from 2D methods push velocities away from negative trajectories without specifying preferred-sample targets; DHO instead dynamically homes negatives toward preferred regions.Source: §2.2 · p. 3

3.1 RECTIFIED FLOW AS POLICY OPTIMIZATION; 3.2 DYNAMIC HOMING OPTIMIZATION

• Rectified flow is treated as a continuous-time policy, while DHO redirects negative trajectories toward preferred samples rather than merely steering away from negative-trajectory directions.The same matching and homing construction also applies to the positive-sample branch.Source: §3.1 · p. 3, §3.2 · p. 4, Figure 3 · p. 4

3.2.1 MINIMUM-COST ATTRACTIVE MATCHING

• MAM uses batchwise minimum-cost one-to-one matching to assign each negative sample a distinct positive target, with reward advantages selecting equally sized positive and negative sets.The assignment is a linear sum assignment solvable by the Hungarian algorithm in O(B^3).Source: §3.2.1 · pp. 4–5, §3.2 · p. 4

3.2.2 TIME-AWARE DYNAMIC CORRECTION

• TDC sets the corrective velocity from the current state to the assigned target and scales it by remaining time, covering residual displacement by t = 1.A time-dependent weight cancels the correction field's endpoint singularity and keeps the regression target smooth across the time horizon.Source: §3.2.2 · p. 5

3.2.3 FULL OPTIMIZATION OBJECTIVE

• The full DHO objective combines negative-trajectory homing, positive-trajectory anchoring, and regularization toward a frozen reference policy.The positive branch's self-matched target reduces its correction to the standard rectified-flow action.Source: §3.2.3 · p. 5, §3.2.2 · p. 5

3.2.4 ENDPOINT BEHAVIOR ANALYSIS

• The endpoint analysis predicts that a negative sample's prior input is redirected to its assigned positive target, with convergence conditional on assignment stabilization.Under the idealized snapshot update, the terminal endpoint interpolates toward that target; MAM may reassign targets across minibatches.Source: §3.2.4 · p. 6

3.2.5 CLASSIFIER-FREE GUIDANCE FOR DHO

• DHO supports classifier-free guidance by using the same guidance scale for rollout generation, policy updates, and inference.The scale balances exploration diversity and generation quality; s = 1 is the CFG-free setting.Source: §3.2.5 · p. 6

3.3 FLOW3D-PRO

• Flow3D-Pro separates image-to-mesh generation into a lifting stage for global geometry and spatial arrangement and a refinement stage for finer details.Post-training focuses on Stage I; Stage II remains frozen and refines its output at inference.Source: §3.3 · pp. 6–7

3.3.1 ASYNCHRONOUS ONLINE DHO

• Asynchronous online DHO decouples mesh rollout and reward evaluation from policy updates, using a replay buffer and discarding data from outdated policy versions.An update-to-buffer constraint balances learning from newly collected rewards against reuse of stale rollout data while the stages run concurrently.Source: §3.3.1 · p. 7

4.1 DATASET

• GenMesh-Test contains 200 challenging reference images, and LATTICE-Bench provides a second evaluation set; both are disjoint from training.GenMesh-Test spans object categories, visual styles, and geometric complexity.Source: §4.1 · p. 7

4.2 IMPLEMENTATION DETAILS

• DHO training used 5K AdamW optimization steps at a learning rate of 2.5 × 10−6, with asynchronous allocation of 28 rollout GPUs and 4 policy-update GPUs.Stage II remained frozen during inference.Source: §4.2 · p. 8

4.3 EVALUATION METRICS

• The evaluation uses ULIP, Uni3D, and a user study, with human experts ranking meshes and the user study prioritized as the primary subjective metric.Source: §4.3 · p. 8

4.4 COMPARISON OF REINFORCEMENT LEARNING OBJECTIVES

• DHO scored higher than other RL methods, especially on the User Study, the primary subjective metric.All RL variants shared the SFT initialization, reward model, GenMesh-Test set, and frozen Stage II refiner; experiments used three seeds and reported means.Source: §4.4 · p. 8, Table 1 · p. 8, §4.3 · p. 8
• GRPO-style, DPO-style, and NFT-style outputs showed implausible or damaged geometry, while these defects persisted after Stage II refinement.Examples include four fingers, a flame-shaped forehead, and a broken staircase; DHO instead achieved better geometry by attraction-guided navigation.Source: §4.4 · pp. 8–9, Figure 5 · p. 8

4.5 COMPARISON WITH EXISTING 3D GENERATION METHODS

• Flow3D-Pro achieved the highest performance among compared methods on all three metrics: 0.150 ULIP, 0.360 Uni3D, and 8.64 User Study.The visual comparison also reports better reference-image adherence, more plausible geometry, and finer details.Source: §4.5 · p. 9, Table 2 · p. 9, Figure 6 · p. 9

5 CONCLUSION

• DHO combines Minimum-Cost Attractive Matching for preferred positive targets with Time-Aware Dynamic Correction to construct homing velocities.Source: §5 · p. 10
• Flow3D-Pro instantiates DHO through asynchronous online post-training for image-to-3D mesh generation.Source: §5 · p. 10
• Experiments report that DHO outperforms representative DPO-, GRPO-, and NFT-style objectives, while Flow3D-Pro surpasses existing methods in geometry quality.Source: §5 · p. 10

A.1 PROOFS FOR ENDPOINT BEHAVIOR ANALYSIS PROPOSITIONS

• Under pointwise contraction toward the homing field, the terminal endpoint moves from the negative sample toward its assigned positive target at a geometric rate.The stated endpoint is x1(τ) = [1 − (1 − α)^τ]xw* + (1 − α)^τxl, converging to xw* as τ grows.Source: §A.1 · pp. 17–18

A.2 REWARD DESIGN

• The reward evaluator scores reconstruction fidelity, geometric plausibility, and orientation alignment from a reference image and six canonical-view renders, then combines them into an integer reward.The three dimensions are weighted 3:2:1; each receives an individual score from 1 to 5.Source: §A.2 · p. 18, Figure 7 · p. 19

A.3 DHO PSEUDOCODE

• DHO ranks rollout samples by group-normalized advantages, balances positive and negative sets, matches pairs, and combines weighted branch losses with reference-policy regularization.MAM uses latent-feature distances and Hungarian assignment; TDC makes the negative-branch regression target account for remaining displacement to the positive endpoint.Source: §A.3 · pp. 19–20

A.4 ROLLOUT SAMPLING

• DHO reconstructs update interpolants from rollout endpoints rather than stored trajectories, allowing ODE or SDE sampling; independent initial noises diversify ODE rollouts, while SDE adds stochastic exploration.For each reference image, either sampler generates a group of meshes for reward evaluation.Source: §A.4 · p. 20

B.1 MORE IMPLEMENTATION DETAILS

• Stage I uses Hunyuan3D 2.1, with 5K SFT steps and 5K DHO optimization steps; Stage II uses LATTICE for structure-conditioned mesh extraction.Stage II remains frozen during geometric refinement at inference.Source: §B.1 · p. 21
• For asynchronous DHO training, 28 GPUs handle rollout and 4 handle policy updates, and SDE sampling is favored for greater rollout diversity.The setup uses a rollout group size of 8 and 50 ODE sampling steps for Stage I inference.Source: §B.1 · p. 21
• RL objective comparisons share the Stage I architecture, SFT initialization, reward model, evaluation set, frozen Stage II refiner, and asynchronous training configuration.All variants train for 5K optimization steps and use 50 ODE inference steps.Source: §B.1 · p. 21

B.2 USER STUDY EVALUATION CRITERIA

• Experts judge fidelity by how recognizably a mesh conveys the reference’s identity and overall proportions.Evaluations are holistic rather than checklist-based.Source: §B.2 · p. 21
• Plausibility concerns whether the generated shape reads as a coherent, well-formed 3D object in its own right.Source: §B.2 · p. 21
• Three experts independently rank anonymized outputs for each reference image; scores are averaged across experts and images.Method identities are hidden and presentation order is randomized for each sample.Source: §B.2 · p. 21

Target assignment

• MAM obtains the highest scores on all three metrics, outperforming soft attraction, random pairing, and nearest-neighbor matching.Soft attraction can retain a diffuse multi-target direction near equilibrium, whereas MAM assigns each negative sample a single positive target under a one-to-one constraint.Source: §B.3 · p. 22, Figure 8 · p. 22

Positive-sample selection and weighting

• Highest-advantage positive selection raises User Study from 0.44 to 0.56, and advantage weighting performs better than treating retained pairs equally.The selection comparison prioritizes the B highest-advantage positives over random selection; weighting scales each positive loss by its normalized positive advantage and transfers that weight to assigned negatives.Source: §B.3 · pp. 22–23, Figure 9 · p. 22, Table 5 · p. 23

Time-aware and dynamic correction

• Time-aware weighting improves ULIP from 0.146 to 0.149, Uni3D from 0.354 to 0.359, and User Study from 0.45 to 0.55; dynamic correction raises User Study from 0.31 to 0.69.The proposed time weighting yields a numerically stable regression target over the full time horizon; dynamic correction accounts for the current state and remaining time, unlike a static action.Source: §B.3 · pp. 22–23, Table 3 · p. 22, Table 4 · p. 23

Classifier-free guidance

• CFG scale s = 3.0 performs better than the CFG-free setting s = 1.0 and the other evaluated guidance scales.The authors describe s = 3.0 as balancing rollout diversity and generation quality during policy optimization.Source: §B.3 · p. 23, Figure 10 · p. 23

Negative homing and reference regularization

• Among tested settings, η = 0.1 and β = 1.0 score highest; removing either negative-sample homing or reference-policy regularization worsens results.The reported results indicate that homing must be balanced with positive-sample anchoring, while reference regularization keeps the policy near the pretrained velocity field.Source: §B.3 · pp. 23–24, Table 6 · p. 24

Rollout settings

• Increasing rollout group size G from 2 to 8 raises User Study score from 0.50 to 1.60, while SDE rollout outperforms ODE sampling, raising User Study from 0.33 to 0.67.SDE yields larger gains in both branches.Source: §B.3 · pp. 24–25

Reward dimensions and runtime

• Reconstruction fidelity yields the largest reward gain, with geometric plausibility and orientation alignment adding improvements; Stage I inference averages 62 s and Stage II refinement 81 s per sample.Both runtimes are reported on an NVIDIA H20 GPU.Source: §B.3 · p. 25, Table 8 · p. 25

Comparison with 3D generators on LATTICE-Bench

• Flow3D-Pro obtains the highest scores among listed representative image-to-3D mesh methods on LATTICE-Bench, reaching 0.140 in ULIP and 0.326 in Uni3D.The passage reports these results after post-training with DHO.Source: §B.4 · p. 25, Table 9 · p. 26

Comparison with additional post-training methods

• On GenMesh-Test, DHO outperforms both rejection fine-tuning (RFT) and PFM.The comparison holds base-generator inference settings and mesh decoding fixed; PFM additionally integrates its preference flow.Source: §B.4 · pp. 25–26, Table 10 · p. 26

Commercial model comparison

• In the shown examples, Flow3D-Pro better preserves facial symmetry and bilateral component consistency than two commercial models while producing plausible global shapes and higher reconstruction fidelity.The examples describe a skewed nose and missing eyeglass lenses for Model 1, and inconsistent launcher layouts and distorted central geometry for Model 2.Source: §B.5 · pp. 26–27

More generation results

• Across diverse categories, displayed examples retain recognizable global silhouettes and category-specific structures alongside local details.Examples include characters, animals, plants, vehicles, architecture, everyday objects, and hard-surface assets.Source: §B.5 · p. 27, Figure 14 · p. 27

Reward design

• Current reward dimensions are not fine-grained enough to accurately reflect higher-precision geometric properties of reference-image-guided meshes.The authors plan to decompose reward dimensions further and collect feedback from more professional artists.Source: C LIMITATIONS AND FUTURE WORK · p. 28

Stage II scope

• DHO is applied only to the lifting stage; the refinement stage remains frozen because its tightly conditioned rollouts have limited diversity for policy optimization.The authors plan to explore ways to enrich Stage II rollout diversity.Source: C LIMITATIONS AND FUTURE WORK · p. 28