Learnings

Introduces Score Distillation Sampling (SDS): how a frozen, pretrained 2D image diffusion model can be turned into a differentiable "does this look right" critic for a NeRF's renders, with no 3D training data and no per-shape neural network training — just gradient descent on a NeRF's own parameters, one random camera view at a time. Covers diffusion models, classifier-free guidance, and the SDS gradient derivation from scratch.

A transformer that turns a point cloud into a clean, quad-dominant, artist-style mesh (≤1600 faces) in a single fast pass — the direct opposite of DreamFusion's per-shape optimization loop. Explains transformers, tokens, embeddings, and autoregressive generation from scratch, plus V2's actual contribution (Adjacent Mesh Tokenization) and why feed-forward 3D generators in general benefit from a higher-quality input shape.

The foundational orientation-field / position-field approach to fast, quad-dominant retopology — works directly on point clouds, no manifold mesh required — using purely local smoothing operators instead of an expensive global solve. Trades global optimality for interactivity; several later papers in this series exist to recover some of that lost optimality.

Keeps Instant Meshes' two fields unchanged, but replaces its greedy local singularity cleanup with an exact minimum-cost-flow solve (plus small local SAT problems for face-orientation consistency) — about 4x fewer singularities than Instant Meshes, still under 10 seconds per model. Explains why removing singularities is fundamentally a discrete bookkeeping problem, and how it's made tractable without NP-hard integer programming.

Solves the representation problem that blocks treating N-way symmetric direction fields like ordinary vectors, unlocking interactive, artist-driven placement, cancellation, and movement of field singularities — instead of only being able to smooth a field and accept wherever singularities land.

Solves for the connection (per-edge parallel-transport rotation) directly, instead of the vector field itself — one sparse linear system gives the smoothest possible field with singularities at exactly the locations and indices you prescribe, no iteration, no manual sculpting required.

A structurally different alternative to every field-based method in this series: quadrangulate an isolated disk-shaped patch given only its own boundary edge counts, guaranteed to succeed for any valid input via a small proven-complete library of topological patterns — no manifold assumption about the rest of the model, no global solve at all.

Learns to predict a quad-dominant mesh directly from a point cloud in one feed-forward pass, instead of solving a fresh field/combinatorial problem per shape — the "MeshAnything V2, but native quads" approach. Explains its triplet-margin contrastive mechanism for associating vertices to faces, and argues generating triangles first and converting to quads afterward is fragile when the triangles are machine-generated rather than clean ground truth. No public code/weights yet.