# Walking the Schr"odinger Bridge: A Direct Trajectory for Text-to-3D Generation

arXiv: https://arxiv.org/abs/2511.05609 · HTML: https://mlsanity.com/paper/2511.05609/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 38 of its 50 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 38)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation](https://mlsanity.com/paper/2303.13873/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Text-to-3D using Gaussian Splatting](https://mlsanity.com/paper/2309.16585/) (2023)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [LucidDreamer: Towards High-Fidelity Text-to-3D Generation via Interval Score Matching](https://mlsanity.com/paper/2311.11284/) (2023)
- [GaussianDreamer: Fast Generation from Text to 3D Gaussians by Bridging 2D and 3D Diffusion Models](https://mlsanity.com/paper/2310.08529/) (2023)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Text-to-3D with Classifier Score Distillation](https://mlsanity.com/paper/2310.19415/) (2023)
- [Delta Denoising Score](https://mlsanity.com/paper/2304.07090/) (2023)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)
- [HiFA: High-fidelity Text-to-3D Generation with Advanced Diffusion Guidance](https://mlsanity.com/paper/2305.18766/) (2023)
- [Noise-Free Score Distillation](https://mlsanity.com/paper/2310.17590/) (2023)
- [DreamTime: An Improved Optimization Strategy for Diffusion-Guided 3D Generation](https://mlsanity.com/paper/2306.12422/) (2023)
- [ShapeCrafter: A Recursive Text-Conditioned 3D Shape Generation Model](https://mlsanity.com/paper/2207.09446/) (2022)
- [DiffSplat: Repurposing Image Diffusion Models for Scalable Gaussian Splat Generation](https://mlsanity.com/paper/2501.16764/) (2025)
- [Score Distillation via Reparametrized DDIM](https://mlsanity.com/paper/2405.15891/) (2024)
- [Rethinking Score Distillation as a Bridge Between Image Distributions](https://mlsanity.com/paper/2406.09417/) (2024)
- [Baking Gaussian Splatting into Diffusion Denoiser for Fast and Scalable Single-stage Image-to-3D Generation and Reconstruction](https://mlsanity.com/paper/2411.14384/) (2024)

## Built on by (most cited first, 3 of 3)

- [Block3D: Efficient Text-to-3D Generation via Block-Wise Diffusion](https://mlsanity.com/paper/2608.19567/) (2026)
- [Sparsely-Supervised Data Assimilation via Physics-Informed Schr"odinger Bridge](https://mlsanity.com/paper/2603.22319/) (2026)
- [CAdam: Context-Adaptive Moment Estimation for 3D Gaussian Densification in Generative Distillation](https://mlsanity.com/paper/2605.20872/) (2026)

## Abstract (arXiv)

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 Schr"odinger Bridge framework. We prove that SDS employs the reverse process of an Schr"odinger 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 Schr"odinger 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.