The Surface Water and Ocean Topography (SWOT) mission provides two-dimensional sea surface height (SSH) snapshots in which mesoscale, submesoscale, and internal-wave signals coexist. Because wave and non-wave components can overlap in horizontal scale and SSH gradients, wave contamination can bias surface-current and energy diagnostics derived from SWOT SSH if it is not separated. Existing decomposition methods typically require continuous time series, complete $(x,y,t)$ data cubes, concurrent velocity fields, or other dynamical variables that are difficult to observe. Spatial filtering can be applied to a single SSH snapshot, but it struggles when the two components overlap in scale. Existing deep-learning methods for wide-swath separation often train on model output cropped into fixed pseudo-SWOT swaths, which prevents full use of native-grid simulation samples.
We propose a conditional implicit neural representation that learns a continuous wave SSH field directly from SSH on the native LLC4320 latitude--longitude grid and can be queried at arbitrary observation coordinates. Training labels are obtained by two-dimensional Lagrangian high-pass filtering of wave SSH at the target time. For SWOT inference, the model conditions on an SSH snapshot, observation coordinates, and static priors, and outputs wave SSH at SWOT coordinates. The corresponding non-wave component is obtained by subtracting the predicted wave SSH from total SSH. This design avoids training on fixed SWOT swath cutouts and confines the expensive physical decomposition to offline label generation. We evaluate the model using SSH errors, gradient and Laplacian diagnostics, wavenumber spectra, and geostrophic-velocity consistency of the residual non-wave SSH. The method combines native-grid physical supervision with a queryable continuous-field representation, providing a transferable modeling route for wave--non-wave separation in SWOT snapshots.