cloneofsimo / consistency_models Goto Github PK

Hello. Why do N(k), m(k) depend on the number of epoch, not on the number of step?

Thanks for the brilliant work! I am reading this legendary paper and get this question that I want to discuss here.

The paper starts at introducing a new method to distill knowledge from a trained score-based model. By Eq. (7) one could easily learn that the function $\boldsymbol f_\theta$ maps two different points to the same result. These two points inherently lie on the same ODE trajectory, as ${\hat{\mathbf x} {t_n}}^{\phi}$ comes from $\mathbf x_{t_{n+1}}$ by a step of score-based ODE. In this way, the function learns to map all the points on an ODE trajectory to the same point, so it can be used to generate data by one direct step from the initial point (Gaussian noise). So far this makes perfect sense to me.

By then the paper starts to introduce "training consistency models in isolation", and the training objective remains almost the same except that the two points become $\mathbf x+{t_{n+1}}\mathbf z$ and $\mathbf x+t_n\mathbf z$. These two points obviously cannot lie in the same ODE trajectory. Otherwise, the ODE trajectory becomes a straight line as they are using the same $\mathbf z$. Eq. (9) states the relationship between loss values of Consistency Distillation and Consistency Training, but this comparison is based on the expectation of all data $\mathbf x$. If my understanding is correct, then when we are using Eq. (10) to train a generative model, the function $\boldsymbol f$ is not intended to learn as the same as in consistency distillation, i.e. map all points in an ODE trajectory to its starting point. If so, what is Eq. (10) really doing and is Fig. 2 still valid in this sense?

I know this is not directly related to this implementation but I'm looking forward to any hint!

Hello! Your work is truly remarkable. I've had the opportunity to experiment with standard DDPM models using DDIM sampling, and despite being relatively slow, they exhibit a fascinating reversibility property. This allows for seamless transitions between Gaussian noise and images, as well as the reverse process, recreating the exact same input noise.

I would be grateful if you could provide some insights into whether this reversibility property is preserved in Consistency models. The examples provided do not explicitly demonstrate this aspect, and I am eager to learn more about it. Thank you for your time and expertise.