One class of methods compute continuous noise levels based on discrete diffusion steps and retrain a new model conditioned on these continuous noise levels (Song and Ermon, 2019; Chen et al., 2020; Okamoto et al., 2021; San-Roman et al., 2021). Then, a shorter reverse process can be obtained by carefully choosing a small set (size S) of noise levels.
reverseproce의 길이를 S<<T steps로 줄이는 방법이다. 학습때보다 reverse의 Step을 줄인다. 하지만 이 방법은 pretrained diffusion model로 다시 사용하는 등 문제가 많다. 또한 속도와 샘플의 퀄리티는 trade off의 관계를 가진다.
Although both classes of methods have shown the trade-off between sampling speed and sample quality (i.e., larger S lead to higher sample quality), the fast sampling methods without retraining are more advantageous for fast iteration and deployment, while still keeping high-fidelity synthesis with small number of steps in the reverse process (e.g., S = 6 in Kong et al. (2020b)).
이 fast sampling이 trade off를 지니지만 retraining 없이 fast samping은 큰 장점을 얻는다.
In this work, we propose FastDPM, a unified framework of fast sampling methods for diffusion models without retraining. The core idea of FastDPM is to i) generalize discrete diffusion steps to continuous diffusion steps, and ii) design a bijective mapping between continuous diffusion steps and continuous noise levels. Then, we use this bijection to construct an approximate diffusion process and an approximate reverse process, both of which have length S <<T.
retraining 없이 빠른 samping 방법의 통합된 framework인 FastDPM을 제안한다. distrete diffusion steos을 continius diffusin step으로 바꾸고 continuous diffusion step과 continuous noise level 사이에 bijective mapping을 한다. 이 bijection 구조는 diffusion process와 revers process 둘다 근사한다.
we propose FastDPM, which approximates the pretrained DDPM via much shorter diffusion and reverse processes of length S T, thus it can generate a sample by only running the network S times. The core idea of FastDPM is to: i) generalize discrete diffusion steps to continuous diffusion steps and, then ii) design a bijective mapping between continuous diffusion steps and continuous noise levels,
FastDPM은 훨씬 짧은 diffusion과 reverse process 길이 S<<T를 통해 pretrained DDPM에 근사한다. 따라서 network는 S times만 학습하고도 생성한다. 주요 아이디어는 discrete에서 continuous diffusion step 그리고 연속 diffusion step과 noise step 사이에 bijective mapping을 한다.
we generalize discrete (integer) diffusion steps to continuous (real-valued) diffusion steps. Then, we introduce a bijective mapping R and T = R−1 between continuous diffusion steps t and noise levels r: r = R(t) and t = T (r).
discrete(integer)에서 continuous하게 바꾸고 bijective mapping을 도입한다.
Define R
sampling xt given x0 is equivalent to adding a Gaussian noise to x0. Based on this observation, we define the noise level at step t as R(t) = √ α¯t, which means xt is composed of R(t) fraction of the data x0 and (1 − R(t)) fraction of white noise. For example, R(t) = 0 means no noise and R(t) = 1 means pure white noise.
동일한 가우시안 노이즈를 추가하는데 step t에 맞는 노이즈 강도를 R(t)로 정의한다. R(t)=0이면 noise가 없는 거고 R(t)=1이면 전부 노이즈라 보면된다.
Next, we extend the domain of R to real values. Assume that the variance schedule {βt} T t=1 is linear: βi = β1 + (i − 1)∆β, where ∆β = βT −β1 T −1 (Ho et al., 2020). We further define an auxiliary constant βˆ = 1−β1 ∆β , which is T assuming that βT <<1.0. 1 Then, we have
Because the Gamma function Γ is well-defined on (0, ∞), Eq. (5) gives rise to a natural extension of α¯t for continuous diffusion steps t. As a result, for t ∈ [0, βˆ), we define the noise level at t as:
