Variable fonts enable continuous variation of glyph geometry along semantic design axes such as weight, width, slant, and optical size. However, constructing a variable font from a static font remains a labor-intensive process requiring expert type design and manual specification of glyph variation data.
We introduce NIV (Neural Axis Variations), a method that automatically converts a static font into a fully functional variable font. Given glyph outlines and a set of desired design axes, NIV predicts per-point displacement fields. The model operates directly on vector glyph geometry and employs a novel \emph{Combinatorial Embedding} mechanism that captures higher-order interactions between multiple axes, enabling consistent multi-axis variation within a unified framework. We train NIV on a newly constructed dataset derived from variable Google Fonts, comprising over one million variation tuples. The resulting model generalizes across unseen codepoints, unseen font styles, high-complexity CJK glyphs, and even out-of-distribution handwriting inputs. The generated outputs are standard variable font files supporting continuous interpolation via existing rendering engines. To facilitate research, we release the dataset, the complete training and inference implementation, and trained models. Beyond typography, our approach demonstrates how structured geometric objects with continuous parametric variation can be modeled and synthesized using neural deformation fields.