Continuous Spatio-Temporal Diffusion on Hamiltonian Manifolds for Real-Time 4D World Synthesis
Contemporary generative video architectures struggle to maintain persistent geometric consistency over extended temporal horizons and routinely violate fundamental conservation principles. We present Nuvi-X DiT-4D, a continuous generative world model operating directly over a 4D spacetime manifold parameterized by Lie algebra \(\mathfrak{se}(3)\) transformations and symplectic Hamiltonian constraints. By training across 180,000 GPU cluster hours on 24 million multimodal trajectories, our system achieves sub-5ms interactive inference latency at 120 FPS while preserving 99.94% energy and momentum conservation across multi-agent environments.
1. Introduction & Mathematical Motivation
Autonomous vehicles, robotic manipulation, and aerospace navigation require predictive world representations that are not only photorealistic but physically faithful. Discretized 2D frame prediction methods introduce accumulation error \(\mathcal{O}(\Delta t^2)\) that causes rapid hallucination. Nuvi-X parameterizes the physical world state as a continuous trajectory in phase space:
Where \(\mathcal{H}(\mathbf{q}, \mathbf{p})\) denotes the learned Hamiltonian representing total kinetic and potential energy of all participating entities in the scene.
2. Multi-Modal Sensorium Decoupling
Unlike video models that produce flattened RGB images, the Nuvi-X latent space directly decodes into four synchronized operational sensor streams:
3. Distributed Tensor Cluster Scaling Laws
Pre-training our 32-billion parameter foundation world model necessitates massive distributed tensor parallelism. Our cluster configuration utilizes 512 matrix acceleration nodes interconnected over 3.2 Tbps non-blocking InfiniBand fabrics:
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