Abstract: Reconstructing intensity frames from event data while maintaining high temporal resolution and dynamic range is crucial for bridging the gap between event-based and the frame-based computer vision. Previous approaches have depended on supervised learning on synthetic data, which lacks interpretability and risk over-fit the setting of the event simulator. Recently, self-supervised learning (SSL) based methods, which primarily utilize per-frame optical flow to estimate intensity via photometric constancy, has been actively investigated. However, they are vulnerable to errors in case of inaccurate optical flow. This paper proposes a novel SSL event-to-video reconstruction approach, dubbed EvINR, which eliminates the need for labeled data or optical flow estimation. Our core idea is to reconstruct intensity frames by directly addressing the event generation model, essentially a partial differential equation (PDE) that describes how events are generated based on the time-varying brightness signals. Specifically, we utilize an implicit neural representation (INR), which takes in spatiotemporal coordinate $(x, y, t)$ and predicts intensity values, to represent the solution of the event generation equation. The INR, parameterized as a fully-connected Multi-layer Perceptron (MLP), can be optimized with its temporal derivatives supervised by events. To make EvINR feasible for online requisites, we propose several acceleration techniques that substantially expedite the training process. Comprehensive experiments demonstrate that our EvINR surpasses previous SSL methods by 38% Mean Squared Error (MSE) and is comparable or superior to SoTA supervised methods.