The paper introduces a phase framework for data distributions connected by local denoisers and demonstrates that reverse diffusion consists of trivial and data phases separated by a transition where local score functions must fail, tied to spatial Markovianity.
We notice thatχ| ϵ=0 =ρ 1 2 and ∂ ∂ϵ (χ−1) ϵ=0 =−(χ| ϵ=0)−1 ∂χ ∂ϵ ϵ=0 (χ|ϵ=0)−1 =−ρ − 1 2 ∂χ ∂ϵ ϵ=0 ρ− 1 2 .(S62) 13 Then we only need to compute ∂χ ∂ϵ ϵ=0
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Local Diffusion Models and Phases of Data Distributions
The paper introduces a phase framework for data distributions connected by local denoisers and demonstrates that reverse diffusion consists of trivial and data phases separated by a transition where local score functions must fail, tied to spatial Markovianity.