For the final sample $x_0$,
there exists infinitely many possible reverse-denoising trajectories
that could have produced under the model.
Diffusion models does not laern one trajectory per sample.
It learns a distribution over trajectories.
Trajectory is a full sequence from $x_T$ to $x_0$ ($x_T \rightarrow x_{T-1} \rightarrow \cdots \rightarrow x_1 \rightarrow x_0$).
Each intermediate $x_t$ is sampled from a probability distribution.
Given a noisy $x_t$, the model outputs a distribution of possible slightly less noisy samples $x_{t-1}$.
When we sampling, we draw from that distribution.
Intuition about diffusion models
Even starting from the same noisy sample $x_T$,
different random draw will produce different trajectories.
The model learns direction that reduces noise. A trajectory is simply what you get
when you follow these learned local transitions step by step.
