Learning Video Dynamics with Predictive Differentiable Rendering

The world evolves following its dynamics, i.e., its laws of motion. However, leading video diffusion models largely fit the pixels without modeling how the pixels transit over time. Thus, they render visually plausible frames but may not accurately obey the laws. To capture the dynamics purely from pixels, we introduce Latent Dynamics Reasoning (LDR). LDR casts the latent transition as an explicit kinematic integration, where the lower-order dynamics are integrated numerically and the model regresses only the third- and higher-order residual that drives the rollout. For this integration to extrapolate better, LDR runs it on a structured latent rather than dense convolutional features. Following PhyWorld, we validate LDR on a controlled white-box physics benchmark spanning five tasks (uniform motion, parabola, collision, bouncing, looming), focusing on out-of-distribution scenarios that reveal whether a model has truly learned the underlying dynamics. LDR extrapolates the learned dynamics far better: the gap between its in- and out-of-distribution error is over 20$\times$ smaller than the video diffusion baseline's, under both single- and joint-task training at 256$^2$ resolution, while using 26$\times$ fewer parameters and running 143$\times$ faster. LDR can even generalize under severe shift: for example, trained only on red balls moving left-to-right, it correctly predicts the motion of a blue square moving right-to-left. To our knowledge, this is the first video world model that extrapolates learned dynamics beyond its training distribution. Project page: https://lat-dyn-reason.github.io/

Pretrained video diffusion models can act as renderers when the desired scene state is already specified by an animated mesh, a camera trajectory, and a reference image. This 4D generative rendering setting raises a representation question: what image-format condition lets a video backbone obey both camera motion and scene-internal animation? We propose DAR, a reference-guided renderer that extends Wan2.2 camera control from Plücker rays alone to a joint camera-plus-geometry interface. DAR projects a neural 4D G-buffer (tracking, world position, and normal) from the animated mesh and injects it through a widened control adapter while preserving the pretrained image-to-video prior. The central design choice is the pair of tracking and world position. Tracking identifies the persistent surface element that should carry appearance; world position gives its current scene-coordinate state; normal supplies local shape. Depth plus calibrated rays can recover 3D in principle, but depth is a camera-dependent chart in which camera and object motion are mixed. On the 68-case DAR-4D benchmark, LoRA DAR reaches PSNR 23.22, SSIM 0.895, and LPIPS 0.134, improving over off-the-shelf Wan2.2-Depth by 1.54 dB PSNR; a full fine-tune reaches PSNR 25.36 and SSIM 0.917. Matched ablations show that replacing world position by depth reduces PSNR by 1.26--1.55 dB at every checkpoint, supporting tracking+world-position correspondence as a practical 4D rendering condition.

World models have become a central paradigm for learning predictive simulators that support generation, planning, and decision-making. Yet, despite rapid progress in industry-scale interactive video generation, the broader research community still lacks compact, reproducible, and easily extensible implementations for studying the design choices underlying modern world models. We introduce Nano World Models, a minimalist codebase for future video prediction centered around diffusion forcing. Nano World Models provides a unified interface for generative objectives, model scales, action-conditioning mechanisms, latent observation spaces, datasets, evaluation protocols, and long-horizon rollout procedures. This design enables controlled studies of world-modeling components that are often entangled across separate implementations. Through experiments across simple control environments, game simulation, and real-robot data, we examine how prediction parameterization, architecture scale, action injection, sampling budget, and domain complexity affect video prediction quality and autoregressive rollout behavior. By releasing code, configurations, evaluation scripts, and pretrained checkpoints, Nano World Models aims to provide a compact yet extensible experimental substrate for open, reproducible, and scientific world-model research.