# Questions tagged [diffusion]

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### simplified form for CDF of inverse Gaussian function, as function of the drift parameter

I am thinking about modelling the probability of an event as a waiting time for a Brownian motion with drift to pass a certain barrier. Then consider what the expression for that probability looks ...
• 80.9k
20 views

### Why reverse diffusion process is not a gaussian distribution?

The forward diffusion process, which goes from x_t to x_{t+1} is Gaussian, which is very reasonable as we go the next state by adding random gaussian noise. However, I do not understand why the ...
• 185
15 views

### Reverse distribution in DDPMs

In Denoising Diffusion Probabilistic Models, we want to reverse a forward process where we blend gaussian noise into a data point $\mathbf{x}_0$ over $T$ steps. The result of each forward step applied ...
• 101
12 views

• 123
536 views

### Why is the square root in the forward process of the Diffusion Model?

I am trying to make sense of the diffusion model (one of the videos I watched https://www.youtube.com/watch?v=HoKDTa5jHvg&t=706s). I came across this formula in the model: This picture clearly ...
• 109
2k views

• 739
1 vote
89 views

### Computing properties of non-uniform random walk/diffusion

I have a lot of numerical data which I'm looking to characterise as a (possibly continuous) random walk with variable (in space) step size, for example, along $x$ between $-1$ and $1$ with a step size ...
• 11
1 vote
273 views

### 2 Dimensional Random Walk Simulation

I am trying to simulate random diffusion of particles using a random walk diffusion model. I have used probabilities of movement of particles in a 2D area, to be 1/4 in all 4 directions. The confusion ...
1 vote
974 views

### confusion about root mean squared distance in 1 dimensional random walk

I was just introduced to the concept of a random walk while reading the Feynman lectures on physics, Volume 1. There was something in the explanation there that confused me, so I tried looking online ...
584 views

### Theoretical link between the graph diffusion/heat kernel and spectral clustering

The graph diffusion kernel of a Graph is the exponential of its Laplacian $\exp(-\beta L)$ (or a similar expression depending on how you define the kernel). If you have labels on some vertices, you ...
• 2,402
583 views

### Diffusion coefficient from double-normal probability density function

The spread of individuals of species is often described by so-called dispersal kernels. The main parameter of spread is then often the variance defined as the average squared movement distance of a ...
• 155
412 views

### What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As ...
• 10.8k