# Spatially-Grounded Text-to-Video Generation via Inference-Time Gradient-Free Optimization

arXiv: https://arxiv.org/abs/2608.13037 · HTML: https://mlsanity.com/paper/2608.13037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Video generation, one of 14 directions in Diffusion models.
- Builds on 47 of its 52 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Placed in

- Diffusion models / [Video generation](https://mlsanity.com/diffusion/video-generation/)

## Builds on (most cited first, 30 of 47)

- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [AnimateDiff: Animate Your Personalized Text-to-Image Diffusion Models without Specific Tuning](https://mlsanity.com/paper/2307.04725/) (2023)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [GLIGEN: Open-Set Grounded Text-to-Image Generation](https://mlsanity.com/paper/2301.07093/) (2023)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [ModelScope Text-to-Video Technical Report](https://mlsanity.com/paper/2308.06571/) (2023)
- [MotionCtrl: A Unified and Flexible Motion Controller for Video Generation](https://mlsanity.com/paper/2312.03641/) (2023)
- [VideoCrafter2: Overcoming Data Limitations for High-Quality Video Diffusion Models](https://mlsanity.com/paper/2401.09047/) (2024)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [InternVid: A Large-scale Video-Text Dataset for Multimodal Understanding and Generation](https://mlsanity.com/paper/2307.06942/) (2023)
- [VideoComposer: Compositional Video Synthesis with Motion Controllability](https://mlsanity.com/paper/2306.02018/) (2023)
- [CameraCtrl: Enabling Camera Control for Text-to-Video Generation](https://mlsanity.com/paper/2404.02101/) (2024)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [OpenVid-1M: A Large-Scale High-Quality Dataset for Text-to-video Generation](https://mlsanity.com/paper/2407.02371/) (2024)
- [Training-Free Layout Control with Cross-Attention Guidance](https://mlsanity.com/paper/2304.03373/) (2023)
- [BoxDiff: Text-to-Image Synthesis with Training-Free Box-Constrained Diffusion](https://mlsanity.com/paper/2307.10816/) (2023)
- [LTX-2: Efficient Joint Audio-Visual Foundation Model](https://mlsanity.com/paper/2601.03233/) (2026)
- [SpaText: Spatio-Textual Representation for Controllable Image Generation](https://mlsanity.com/paper/2211.14305/) (2022)
- [Motion Prompting: Controlling Video Generation with Motion Trajectories](https://mlsanity.com/paper/2412.02700/) (2024)
- [Direct-a-Video: Customized Video Generation with User-Directed Camera Movement and Object Motion](https://mlsanity.com/paper/2402.03162/) (2024)

## Abstract (arXiv)

Diffusion Transformer Text-to-Video models have achieved remarkable synthesis quality, yet fine-grained spatial controllability remains a significant challenge. While existing training-free methods produce solid overall results in spatially grounded generation, ie, placing a specific object in a designated location, they rely on gradient-based optimization techniques that incur prohibitive computational overhead, a bottleneck amplified in modern large-scale architectures. To address this limitation, we present Gradient-free Analytical Trajectory Optimization Video Generation (GATO-Vid), a novel training-free and gradient-free approach for precise spatial guidance. Rather than relying on costly backward passes, we introduce an alternative cross-attention score and solve it analytically to obtain an exact, closed-form solution. To use our analytical solution, we propose an on-the-fly injection mechanism tailored to the topological manifold of the transformer's latent space. Our experiments demonstrate that GATO-Vid significantly outperforms existing baselines in localization accuracy while introducing minimal computational overhead.