From Global to Factor-Wise Expert Composition in Discrete Diffusion Models
Paper Guide Brief
Reading Brief
Proposes FactorDiff, a factor-wise composition framework for discrete diffusion models that routes each spatial factor (pixel) to the most competent expert via confidence-based selection, outperforming global scalar weighting on ARC-AGI.
Central Claim
FactorDiff introduces per-pixel expert routing for discrete diffusion models, enabling spatially heterogeneous composition that captures complementary expert specializations, validated on ARC-AGI.
Contribution
FactorDiff introduces per-pixel expert routing for discrete diffusion models, enabling spatially heterogeneous composition that captures complementary expert specializations, validated on ARC-AGI.
Why It Matters
By decomposing composition into per-factor routing rather than per-sample scalar weighting, FactorDiff allows experts to contribute only where they are locally reliable, achieving large gains when composing specialists (e.g., 90.5% exact a...
Prerequisites
factor-wise composition, per-pixel routing, confidence-based selection, masked diffusion, 2D grid diffusion
Atlas Placement
Deep Learning (subfield)
Read If
You care about factor-wise composition, per-pixel routing, confidence-based selection.
Skip If
You only care about ARC-AGI-1, ARC-AGI.
Noosaga Placements
- The paper proposes a new method for composing discrete diffusion models, a core deep learning technique, and evaluates it on a reasoning benchmark.Discrete diffusion models offer a powerful framework for solving complex reasoning tasksWe propose FactorDiff – a factor-wise composition framework for diffusion models
- Diffusion Modelsframework95%The paper extends discrete diffusion models by introducing a factor-wise composition mechanism (FactorDiff) that goes beyond existing per-sample scalar weighting methods.We propose FactorDiff – a factor-wise composition framework for diffusion modelsWe instantiate this framework with spatial/pixel-level compositions
- The work involves combining multiple pre-trained models (experts) at inference time, a machine learning composition problem, but the core novelty is in the diffusion sampling process.compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data
Abstract
Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.
Paper Context
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