Flow Duality and Source Geometry for Categorical Generation — Paper

Abstract

Continuous and discrete flow matching are usually treated as separate constructions. This paper identifies a duality between them: projecting continuous convex-interpolant paths with one-hot targets through a position-wise argmax yields discrete convex-interpolant paths. The result requires source laws with appropriate coordinate symmetry and boundary regularity, and it makes the continuous source distribution an explicit design choice for categorical generation. We derive the induced discrete interpolation behavior for Gaussian, bounded-uniform, and centered negative-exponential sources, showing that different source geometries lead to qualitatively different transition timing and vocabulary-size dependence. Small visual diagnostics and a short language-modeling pilot suggest that these source-design effects can also appear in learned transports and early generative quality.

Authors 1

Etrit Haxholli

Specification

Official page: arxiv.org/abs/2609.10863
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Arxiv announce type: new
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
arXiv id: 2609.10863
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Categories: cs.LG, stat.ML
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
PDF: arxiv.org/pdf/2609.10863
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh

Each value shows its source, tier and observation time. Conflicting claims are kept side by side and flagged — never averaged. How AI Atlas records facts →

Provenance

Attributed facts

9

Source tiers

T19

Freshest observation

34 min ago

Conflicts

None

No models linked to this paper yet.

Authors: Etrit Haxholli

As of

Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.

Claim history · Abstract

1 claims · 1 propertiesShow all properties

Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
Continuous and discrete flow matching are usually treated as separate constructions. This paper identifies a duality between them: projecting continuous convex-interpolant paths with one-hot targets through a position-wise argmax yields discrete convex-interpolant paths. The result requires source laws with appropriate coordinate symmetry and boundary regularity, and it makes the continuous source distribution an explicit design choice for categorical generation. We derive the induced discrete interpolation behavior for Gaussian, bounded-uniform, and centered negative-exponential sources, showing that different source geometries lead to qualitatively different transition timing and vocabulary-size dependence. Small visual diagnostics and a short language-modeling pilot suggest that these source-design effects can also appear in learned transports and early generative quality.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperFlow Duality and Source Geometry for Categorical Generation
New paper: Flow Duality and Source Geometry for Categorical Generation
arxiv
rss.arxiv.org

Full timeline →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	34 min ago	1

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.