FluidWorld: Reaction-Diffusion Dynamics as a Predictive Substrate for World Models

TL;DR

FluidWorld introduces a PDE-based world model that predicts future states using reaction-diffusion dynamics, offering a computationally efficient alternative to Transformer-based predictors with comparable or better performance.

Contribution

The paper demonstrates that reaction-diffusion PDEs can serve as an effective and efficient computational substrate for world modeling, challenging the necessity of self-attention mechanisms.

Findings

FluidWorld achieves lower reconstruction error than Transformer and ConvLSTM baselines.

It maintains coherent multi-step rollouts where baselines fail.

PDE-based dynamics offer O(N) complexity and global spatial coherence.

Abstract

World models learn to predict future states of an environment, enabling planning and mental simulation. Current approaches default to Transformer-based predictors operating in learned latent spaces. This comes at a cost: O(N^2) computation and no explicit spatial inductive bias. This paper asks a foundational question: is self-attention necessary for predictive world modeling, or can alternative computational substrates achieve comparable or superior results? I introduce FluidWorld, a proof-of-concept world model whose predictive dynamics are governed by partial differential equations (PDEs) of reaction-diffusion type. Instead of using a separate neural network predictor, the PDE integration itself produces the future state prediction. In a strictly parameter-matched three-way ablation on unconditional UCF-101 video prediction (64x64, ~800K parameters, identical encoder, decoder, losses, and data), FluidWorld is compared against both a Transformer baseline (self-attention) and a ConvLSTM baseline (convolutional recurrence). While all three models converge to comparable single-step prediction loss, FluidWorld achieves 2x lower reconstruction error, produces representations with 10-15% higher spatial structure preservation and 18-25% more effective dimensionality, and critically maintains coherent multi-step rollouts where both baselines degrade rapidly. All experiments were conducted on a single consumer-grade PC (Intel Core i5, NVIDIA RTX 4070 Ti), without any large-scale compute. These results establish that PDE-based dynamics, which natively provide O(N) spatial complexity, adaptive computation, and global spatial coherence through diffusion, are a viable and parameter-efficient alternative to both attention and convolutional recurrence for world modeling.