  Anatomical trees play a central role in clinical diagnosis and treatment
planning. However, accurately representing anatomical trees is challenging due
to their varying and complex topology and geometry. Traditional methods for
representing tree structures, captured using medical imaging, while invaluable
for visualizing vascular and bronchial networks, exhibit drawbacks in terms of
limited resolution, flexibility, and efficiency. Recently, implicit neural
representations (INRs) have emerged as a powerful tool for representing shapes
accurately and efficiently. We propose a novel approach, $TrIND$, for
representing anatomical trees using INR, while also capturing the distribution
of a set of trees via denoising diffusion in the space of INRs. We accurately
capture the intricate geometries and topologies of anatomical trees at any
desired resolution. Through extensive qualitative and quantitative evaluation,
we demonstrate high-fidelity tree reconstruction with arbitrary resolution yet
compact storage, and versatility across anatomical sites and tree complexities.
The code is available at:
\texttt{\url{https://github.com/sinashish/TreeDiffusion}}.
