The paper introduces FuNVol, a generative model for simulating multi-asset implied volatility (IV) surfaces over time. The approach combines functional data analysis (FDA) with neural stochastic differential equations (SDEs) to produce realistic market scenarios. First, IV surfaces are projected onto a set of Legendre basis functions, and functional principal component analysis (FPCA) reduces the dimensionality, yielding a time series of functional principal component coefficients (FPCCs). These coefficients, along with other market observables (e.g., asset prices), are then modeled using a neural SDE, where the drift and diffusion are parameterized by GRU-based neural networks. A novel probability integral transform (PIT) penalty is applied during training to reduce model misspecification. The model does not impose explicit static arbitrage constraints, yet the generated surfaces are shown to have less static arbitrage than the training data. The authors validate the model by simulating IV surfaces for four equity tickers and performing a delta hedging exercise, demonstrating that the simulated profit and loss distributions match those from historical data. This framework is useful for generating synthetic data for training reinforcement learning algorithms in hedging and portfolio optimization.