First, why does solving probability flow ODE provide much higher sample quality than solving SDEs, when the number of steps is small? Second, it is shown that stochastic DDIM reduces to marginal-equivalent SDE [42], but its discretization scheme and mechanism of acceleration are still unclear. Finally, can we generalize DDIMs to other DMs and achieve similar or even better acceleration results?
Equipped with this new interpretation, we extend DDIM to general DMs, which we coin generalized DDIM (gDDIM). With only a small but delicate change of the model parameterization, gDDIM can accelerate DMs based on general diffusion processes.
: 1) We provide an interpretation for the DDIM and unravel the mechanism of it. 2) The interpretation not only justifies the numerical discretization of DDIMs but also provides insights on why ODE-based samplers are preferred over SDE-based samplers when NFE is low. 3) We propose gDDIM, a generalized DDIM that can accelerate a large class of DMs. 4) We show by extensive experiments that gDDIM can drastically improve sampling quality/efficiency almost for free.
CLD: In Dockhorn et al. [5] the authors propose critically-dampled Langevin diffusion (CLD), a DM based on an augmented diffusion with an auxiliary velocity term. More specifically, the state of the diffusion in CLD is of the form u(t) = [x(t), v(t)] ∈ R 2d with velocity variable v(t) ∈ R d . The CLD employs the forward diffusion Eq (1) with coefficients
Compared with most other DMs such as DDPM that inject noise to the data state x directly, the CLD introduces noise to the data state x through the coupling between v and x as the noise only affects the velocity component v directly. It is argued that this property improves the performance of DMs [5]. It is observed in Dockhorn et al. [5] that CLD has more efficient noising and denoising processes and can generate high-quality samples with less NFEs compared with DDPM.
The complexity of sampling from a DM is proportional to the NFEs used to numerically solve Eq (6). To establish a sampling algorithm with a small NFEs, we ask the bold question: Can we generate samples accurately from a DM with finite steps if the score function is precise?
