Title: Walking the Schrödinger Bridge: A Direct Trajectory for Text-to-3D Generation
Venue: NeurIPS 2025
Accepted: yes
Keywords: Generative Models

Text-to-3D

3D Gaussian Splatting

Diffusion Models
Abstract: Recent advancements in optimization-based text-to-3D generation heavily rely on distilling knowledge from pre-trained text-to-image diffusion models using techniques like Score Distillation Sampling (SDS), which often introduce artifacts such as over-saturation and over-smoothing into the generated 3D assets. In this paper, we address this essential problem by formulating the generation process as learning an optimal, direct transport trajectory between the distribution of the current rendering and the desired target distribution, thereby enabling high-quality generation with smaller Classifier-free Guidance (CFG) values. At first, we theoretically establish SDS as a simplified instance of the Schrödinger Bridge framework. We prove that SDS employs the reverse process of an Schrödinger Bridge, which, under specific conditions (e.g., a Gaussian noise as one end), collapses to SDS's score function of the pre-trained diffusion model. Based upon this, we introduce Trajectory-Centric Distillation (TraCe), a novel text-to-3D generation framework, which reformulates the mathematically trackable framework of Schrödinger Bridge to explicitly construct a diffusion bridge from the current rendering to its text-conditioned, denoised target, and trains a LoRA-adapted model on this trajectory's score dynamics for robust 3D optimization. Comprehensive experiments demonstrate that TraCe consistently achieves superior quality and fidelity to state-of-the-art techniques. Our code will be released to the community.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Trajectory-Centric Distillation (TraCe), a new framework for text-to-3D generation that reformulates the Score Distillation Sampling (SDS) approach under the Schrödinger Bridge framework. By utilizing LoRA adaptation and an annealed sampling schedule, TraCe mitigates over-saturation and over-smoothing artifacts that often occur with high classifier-free guidance (CFG) values in existing methods.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n- The paper provides a theoretical analysis connecting SDS to Schrödinger Bridge, which offers a fresh perspective on optimization-based 3D generation.\n- Mathematical descriptions, especially of the bridge construction and gradient computation, are clearly presented and well supported by visual diagrams.\n\n# Weaknesses\n- Although the paper claims that the proposed Trajectory-Centric Distillation effectively mitigates over-saturation and over-smoothing artifacts, the qualitative results do not convincingly demonstrate a clear superiority in visual quality. Specifically, it is unclear why Figure 4 does not use exactly the same text prompts and view settings as related works for direct comparison. In both Figure 4 and the Appendix, the results produced by Trajectory-Centric Distillation still exhibit noticeable smoothness and blurriness.\n\n- The experimental setup appears questionable. While the main focus of the method is to improve text fidelity, the quantitative evaluation primarily relies on CLIP Score, which mainly reflects text-image alignment and does not adequately assess texture or geometric fidelity. Moreover, the visual results seem weaker than those in prior works, and the implementation details provided are insufficient, raising concerns about the fairness and reproducibility of the experiments.\n\n- All experiments are conducted exclusively on Gaussian representations, and it remains unclear whether the proposed TraCe framework can outperform VSD when using NeRF representations.\n\nQUESTIONS:\n1. The experimental setup raises concerns. In Table 1, the reported optimization time for VSD is questionable. In NeRF-based representations, VSD typically requires at least 2.5 hours per object, and even with Gaussian representations, it is unlikely for the training time to be shorter than that of ISM. Moreover, the default optimization steps for related methods are generally around 5000, whereas this work only uses 1700 steps, which may artificially reduce the reported optimization time. Even though incorporating LoRA may significantly increase training time, it is important to ensure that each model is fully converged before making fair comparisons.\n\n2. The chosen evaluation metric (CLIP Score) does not align well with the stated motivation of improving texture quality and overall visual fidelity. CLIP primarily measures text-image alignment and cannot sufficiently evaluate texture quality. To support the claims more robustly, it would be more appropriate to incorporate human-aligned evaluation protocols, following GPT-4V(ision) or T^3Bench.\n\n3. The paper lacks comparisons with some closely related and recent works, such as:\nConsistent3D: Towards Consistent High-Fidelity Text-to-3D Generation with Deterministic Sampling Prior\nDreamer XL: Towards High-Resolution Text-to-3D Generation via Trajectory Score Matching\n\n4. The ablation study lacks quantitative evaluation, making it difficult to rigorously assess the contribution of each component. Additionally, the distinction between the naive bridge and the proposed TraCe remains unclear. From my understanding, both approaches appear to rely on Equation (4) to update the 3D representation. Furthermore, the role of LoRA seems limited to color correction, yet incorporating LoRA significantly increases optimization time. This raises questions about whether the additional complexity and computational cost introduced by LoRA are justified by corresponding performance gains.\n\nLIMITATIONS:\nThis work lacks a discussion about limitations and failure cases.\n- Please analyse failure cases.\n- Sensitivity to LoRA fine-tuning stability and the risk of underfitting or mode collapse.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nSummary:\n\nThe paper theoretically establishes Score Distillation Sampling (SDS) as a simplified instance of the Schrödinger Bridge and introduces the TraCe framework, which enables more stable 3D optimization. Experiments demonstrate that TraCe outperforms existing methods in terms of visual quality and text alignment.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThis paper presents quantitative and qualitative comparisons with other methods.\n\nWeaknesses：\n\n1、A related work has proved that Score-based Generative Model (SGM) is a special case of Schrödinger Bridge [1]. \n\n2、This work adopts the tractable Schrödinger Bridge (SB) framework introduced in related work. \n\n3、The results of the proposed method have still artifacts such as over-saturation and over-smoothing.\n\n4、The paper lacks a comparison with Dreamflow[2].\n\n5、There are formatting issues in the references, e.g., Reference 26.\n\n[1] Liu, Guan-Horng, et al. \"I $^ 2$ SB: Image-to-Image Schr\\\" odinger Bridge.\" arXiv preprint arXiv:2302.05872 (2023).\n\n[2]Lee, Kyungmin, Kihyuk Sohn, and Jinwoo Shin. \"Dreamflow: High-quality text-to-3d generation by approximating probability flow.\" arXiv preprint arXiv:2403.14966 (2024).\n\nQUESTIONS:\n1、Please clarify the novelty of the proposed work.\n\n2、Please clarify the differences between this work and prior works with similar ideas, such as DreamFlow [2] and I²SB [1].\n\n3、Why the generated results still have artifacts such as over-saturation and over-smoothing?\n\n[1] Liu, Guan-Horng, et al. \"I $^ 2$ SB: Image-to-Image Schr\\\" odinger Bridge.\" arXiv preprint arXiv:2302.05872 (2023).\n\n[2]Lee, Kyungmin, Kihyuk Sohn, and Jinwoo Shin. \"Dreamflow: High-quality text-to-3d generation by approximating probability flow.\" arXiv preprint arXiv:2403.14966 (2024).\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles the problem of artifacts such as over-saturation and over-smoothing in SDS optimization-based text-to-3D generation methods by theoretically connecting SDS to the Schrödinger Bridge framework and showing that SDS is a simplified instance of this optimal transport approach. The authors introduce Trajectory-Centric Distillation (TraCe), which explicitly constructs a diffusion bridge between current renderings and their text-conditioned targets, training a LoRA-adapted model on the trajectory's score dynamics to enable high-quality generation with smaller Classifier-free Guidance values.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n- The paper is well-written, highly organized and easy to follow.\n- The contribution of the paper in interpreting SDS in the perspective of Schrödinger Bridge is novel, robust and significant, providing meaningful contribution to the field of score distillation based 2D / 3D generation. Theoretical explanation and proof of this interpretation, provided in the paper is robust and sound.\n- The authors translate this interpretation to the methodology well, using the rendered image $x_{rndr}$ and one-step denoised image $x_{0}^{pred}$ as two endpoints of the Schrödinger Bridge and formulating the optimization process as interpolation of two diffusion denoising paths. \n\n**Weaknesses:**\n- The improvement from this method, shown in the experimental section of the paper, seems to be somewhat marginal, unable to achieve meaningful modification in overall geometry but only in texture. Can the authors provide examples in which i) baseline result produces divergent 3D scene (such as Janus problem) but TraCe results in significant improvements from it, or ii) results in which generated result's geometry and layout differs significantly due to usage of TraCe? This seems to be my main concern with the paper, and if this point is elaborated (regarding specifically *how* TraCe improves upon SDS process in implementation), I would raise my score toward acceptance.\n- Both quantitative and qualitative results seem to be lacking in the main paper: can additional experiments (especially qualitative) be provided to back up that TraCe is effective in practice and not only in theory?\n- The paper is unclear in how the LoRA-adapted model $\\epsilon_\\phi(x_t, t, y, c)$ is trained to predict the noise from $x_t$ to $x_{0}^{pred}$: please elaborate. Is it trained online during optimization like LoRA-adapted model in ProlificDreamer (that does seem to be likely)? If this is the case, can this method be seen as a variant of VSD under single-particle setting?\n\nQUESTIONS:\nPlease see the weaknesses section.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Trajectory-Centric Distillation (TraCe), a new optimization framework for text-to-3D generation. The authors establish a theoretical connection between Score Distillation Sampling (SDS) and Schrödinger Bridge (SB) problems, showing SDS as a special case. They then leverage this connection to construct a mathematically principled diffusion bridge between the current rendering and a text-aligned target image. Using this bridge, they train a LoRA-adapted diffusion model to guide 3D optimization, demonstrating superior performance, especially at lower CFG values, compared to existing state-of-the-art methods like SDS, VSD, and SDI.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Establishing that SDS is a special case of the Schrödinger Bridge can provide theoretical insights to the community.\n\n2. Experiments (quantitative and qualitative) demonstrate that TraCe outperforms baseline methods in fidelity, detail, and texture quality, especially at low CFG values.\n\n3. The paper includes qualitative ablations to show the effectiveness of each component.\n\nWeaknesses:\n\n1. The paper heavily relies on CLIP scores, which may not fully capture geometry quality or 3D consistency. Adding metrics like FID on rendered views and 3D metrics would strengthen the claims. Consider moving the human study results from the supplementary to the main manuscript.\n\n2. A more comprehensive quantitative comparison with recent state-of-the-art 3D generation methods is needed.\n\n3. The diversity of the generated objects appears limited and could be further improved.\n\nQUESTIONS:\n1. It's unclear how significant the adaptation via LoRA is. How much of the improvement is from using the SB trajectory versus simply adapting the diffusion model?\n\n2. The 2D experiments show blurry results. Could more analysis be added regarding this?\n\nLIMITATIONS:\nMore description about the limitations should be added.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}