# GeodesicNVS: Probability Density Geodesic Flow Matching for Novel View Synthesis

arXiv: https://arxiv.org/abs/2603.01010 · HTML: https://mlsanity.com/paper/2603.01010/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 46 of its 58 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 46)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [SyncDreamer: Generating Multiview-consistent Images from a Single-view Image](https://mlsanity.com/paper/2309.03453/) (2023)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Make-It-3D: High-Fidelity 3D Creation from A Single Image with Diffusion Prior](https://mlsanity.com/paper/2303.14184/) (2023)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [RealFusion: 360deg Reconstruction of Any Object from a Single Image](https://mlsanity.com/paper/2302.10663/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [EscherNet: A Generative Model for Scalable View Synthesis](https://mlsanity.com/paper/2402.03908/) (2024)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Free3D: Consistent Novel View Synthesis without 3D Representation](https://mlsanity.com/paper/2312.04551/) (2023)
- [Hume: Introducing System-2 Thinking in Visual-Language-Action Model](https://mlsanity.com/paper/2505.21432/) (2025)
- [Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modelling](https://mlsanity.com/paper/2404.12940/) (2024)
- [Boosting Latent Diffusion with Flow Matching](https://mlsanity.com/paper/2312.07360/) (2023)
- [FlowR: Flowing from Sparse to Dense 3D Reconstructions](https://mlsanity.com/paper/2504.01647/) (2025)

## Built on by (most cited first, 2 of 2)

- [SpatialReward: Verifiable Spatial Reward Modeling for Fine-Grained Spatial Consistency in Text-to-Image Generation](https://mlsanity.com/paper/2603.22228/) (2026)
- [CNMBI: Determining the Number of Clusters Using Center Pairwise Matching and Boundary Filtering](https://mlsanity.com/paper/2603.26744/) (2026)

## Abstract (arXiv)

Recent advances in generative modeling have substantially enhanced novel view synthesis, yet maintaining consistency across viewpoints remains challenging. Diffusion-based models rely on stochastic noise-to-data transitions, which obscure deterministic structures and yield inconsistent view predictions. We advocate a Data-to-Data Flow Matching framework that learns deterministic transformations between paired views, enhancing view-consistent synthesis through explicit data coupling. Building on this, we propose Probability Density Geodesic Flow Matching (PDG-FM), which aligns interpolation trajectories with density-based geodesics of a data manifold. To enable tractable geodesic estimation, we employ a teacher-student framework that distills density-based geodesic interpolants into an efficient ambient-space predictor. Empirically, our method surpasses diffusion-based baselines on Objaverse and GSO30 datasets, demonstrating improved structural coherence and smoother transitions across views. These results highlight the advantages of incorporating data-dependent geometric regularization into deterministic flow matching for consistent novel view generation.