# Schr"odinger's Cat: Probabilistic Representation and Prediction of Potential Scene Kinematics

arXiv: https://arxiv.org/abs/2607.25984 · HTML: https://mlsanity.com/paper/2607.25984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 60 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 30 of 44)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [BridgeData V2: A Dataset for Robot Learning at Scale](https://mlsanity.com/paper/2308.12952/) (2023)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [OpenVid-1M: A Large-Scale High-Quality Dataset for Text-to-video Generation](https://mlsanity.com/paper/2407.02371/) (2024)
- [Diffusion for World Modeling: Visual Details Matter in Atari](https://mlsanity.com/paper/2405.12399/) (2024)
- [Unifying Flow, Stereo and Depth Estimation](https://mlsanity.com/paper/2211.05783/) (2022)
- [Unified World Models: Coupling Video and Action Diffusion for Pretraining on Large Robotic Datasets](https://mlsanity.com/paper/2504.02792/) (2025)
- [Rotary Position Embedding for Vision Transformer](https://mlsanity.com/paper/2403.13298/) (2024)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Motion-I2V: Consistent and Controllable Image-to-Video Generation with Explicit Motion Modeling](https://mlsanity.com/paper/2401.15977/) (2024)
- [Training Agents Inside of Scalable World Models](https://mlsanity.com/paper/2509.24527/) (2025)
- [Koala-36M: A Large-scale Video Dataset Improving Consistency between Fine-grained Conditions and Video Content](https://mlsanity.com/paper/2410.08260/) (2024)
- [CoTracker3: Simpler and Better Point Tracking by Pseudo-Labelling Real Videos](https://mlsanity.com/paper/2410.11831/) (2024)
- [Track2Act: Predicting Point Tracks from Internet Videos enables Generalizable Robot Manipulation](https://mlsanity.com/paper/2405.01527/) (2024)
- [Epona: Autoregressive Diffusion World Model for Autonomous Driving](https://mlsanity.com/paper/2506.24113/) (2025)
- [VDT: General-purpose Video Diffusion Transformers via Mask Modeling](https://mlsanity.com/paper/2305.13311/) (2023)
- [Conditional Generative Neural System for Probabilistic Trajectory Prediction](https://mlsanity.com/paper/1905.01631/) (2019)

## Abstract (arXiv)

Predicting how a scene may evolve from partial observations requires reasoning about multiple possible futures rather than committing to a single trajectory. Existing approaches either generate appearance-dominated video predictions or sample a small number of trajectories without explicitly modeling the distribution of possible motion. We introduce Goal-Aware Representations of Future kInEmatic Latent Distributions (GARFIELD), a probabilistic model of scene kinematics that learns a structured spatio-temporal latent representation of the distribution over possible futures given an image and optional spatio-temporally sparse constraints. The same latent representation enables both joint sampling of all trajectories and direct access to the underlying motion distribution through an efficient deterministic density decoder. As a result, uncertainty about future motion can be localized to specific scene elements and timesteps and progressively refined through additional constraints. Experiments demonstrate strong motion planning performance competitive with large video generation models while sampling trajectories 97× faster. Our method further estimates motion densities two orders of magnitude faster than Monte-Carlo sampling from motion generation models, enabling interactive exploration and uncertainty-aware planning.