Questions tagged [diffusion]
The diffusion tag has no usage guidance.
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What kind of Neural Networks are required for Diffusion models?
It appears that regular feed-forward and convolutions are not enough to make diffusion models work (from some personal limited testing, they do not work at all). The typical infrastructure was a U-Net ...
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Can Denoising Diffusions only learn white noise, and/or no drift?
I understand that it works best for image generation to add white noise and no drift because is simpler.
My question is, theoretically speaking, can the noise follow a certain distribution and the ...
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What are the similarities and the differences between MaskGit and Diffusion models
maskgit and diffusion - can you explain the similarities and differences between these two types of models?
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Reparameterization of Poisson Distribution
In deep learning, especially generative models, sometimes we need to add some random noise to the input of model. To make the sampling of random noise learnable (or differentiable), we need to ...
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Confusion with the "lower bound"-term in diffusion models
I am trying to understand the maths of diffusion models following this video explanation on youtube and this blog post.
Here is what how I understood it so far:
The overall goal is, that we want to ...
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VAE with only forward diffusion enhancement ** experiment **
I wanted to get some opinions with an idea that I have explored for a little bit. This is an experiment and I would like to know if this is mathematically plausible or not.
Imagine $\bar{x}$ is the ...
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Blurring of image in generative model using diffusion probabilistic method
In the 2015 paper "Deep Unsupervised Learning using Nonequilibrium Thermodynamics" by Sohl-Dickstein et al. on diffusion for generative models, Figure 1 shows the forward trajectory for a 2-...
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Parameterizing a Gaussian distribution
I am reading this blog post where the author talks about diffusion models. Let's keep diffusion out of the conversation for now. The author showcased that we can parameterize a Gaussian distribution ...
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Justification of the fixed variational distribution in diffusion models
Diffusion models can be regarded as latent variable models (Ho et al., 2020; Section 2), with the latents being an hierarchical chain of random variables $z_T → \dots → z_t → z_{t-1} → \dots → z_1$ (...
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How to rewrite DreamBooth loss in terms of $\epsilon$-prediction?
I'm trying to make the loss used in DreamBooth paper explicit, writing it in terms of the noise, as it is commonly written in the original diffusion article [1], instead of the image reconstruction ...
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Purpose of scaling mean by $\sqrt{1 - \beta_t}$ in forward diffusion process
In the forward diffusion process described by Ho, et al. the probability distribution for the next step is:
$$q(\mathbf{x}_t|\mathbf{x}_{t-1}) = N(\mathbf{x}_t;\sqrt{1-\beta_t}\mathbf{x}_{t-1},\beta_t\...
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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 ...
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Diffusion Models - modeling noise?
In this post about diffusion models, IIUC, we want to use a neural network to approximate the mean of the reverse diffusion: $p_\theta(\mathbf{x}_{t-1} \vert \mathbf{x}_t) = \mathcal{N}(\mathbf{x}_{t-...
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How is the variance for a diffusion kernel derived for a diffusion model?
So I'm watching this video tutorial from CVPR this year on diffusion models, and I am confused by the variance term in the distribution on the left on the video. I understand that in the forward ...
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ELOB (evidence lower bound) for diffusion
I am trying to understand the loss definition for diffusion, but lots of questions already arise during the first step of the derivation. (I have nearly zero statistic knowledge, but I am good at ...
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What is the exact role of model $p_\theta$ in Diffusion models for the reverse process?
I'm reading this interesting blog post explaining Diffusion probabilistic models and trying to understand the following.
In order to compute the reverse process, we need to consider the posterior ...
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Understanding why volatility in diffusion process $(X_t)_{t \in[0,T]}$ is identifiable/known for continuous observations, but the drift is not?
Why is it that when dealing with continuous time observations of a diffusion process $(X_t)_{t \in[0,T]}$, we say that the volatility $\sigma^2$ is "perfectly identifiable" and just usually ...
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Sampling distribution of GBM Maximum-Likelihood estimator
Given the geometric Brownian diffusion
$$ X_t = \mu X_t \, dt + \sigma X_t \, d W_t$$
I learnt that its maximum likelihood estimators are the following as this web article suggests
$$\hat \mu = \frac{\...
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Jump diffusion -advantages
What would people say is the advantage of using a Merton jump-diffusion model, in terms of what it models and it's key characteristics/ features?
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How are differential equations and stochastic differential equations different?
In the simplest terms, how are differential equations and stochastic differential equations different?
As far as I can tell, SDEs are PDEs or ODEs, where the derivative of some function wrt itself is ...
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Carré du champ operator is a quadratic variation
Let $X_t$ be a real valued Markov process (starting at $x$) with generator $L$. Let $\Gamma(f)$ denote Carré du champ operator i.e. $L(f^2) - 2f \cdot L (f)$. As far as I know under suitable ...
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Fit drift diffusion model with trial-type dependent input strength
I want to fit a drift diffusion model to a task which involves multiple decisions (n=400) between two different valuable choice options . I do understand how I would do that in general, also with the ...
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What is the likelihood function of the starting time of diffusion?
I need to find the likelihood that a set of molecules was instantaneously released at time $t_0$, say $t_0=0$.
Toy System Example:
Let $N$ be the set of molecules released from a specific point in a ...
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How to apply the diffusion maps when the matrix is PSD but not positivity preserving?
In order to apply the diffusion maps in a matrix $C\in\mathbb R^{n\times n}$ , that matrix must obey some restrictions,
C is symmetric: $C_{ij} = C_{ji}$,
C is positivity preserving (PP): $\forall ...
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Diffusion tensor as a covariance matrix
TLDR: In nuclear magnetic resonance (NMR), to study molecular diffusion we assume that molecules displace in 3D space according to a trivariate gaussian distribution. The variables are then the ...
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What is the distribution of the peak time of the first hitting time process
I need to find the distribution of the random variable $T_{peak}$ where $T_{peak}$ represents the peak time of the first hitting time process.
Detailed Explanation of the System:
There are $N^{Tx}$ ...
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Stochastic Differential equation: CAPM
Let $R = (R_1, \dots , R_M)'$ denote a vector of excess returns of $M$ assets observed at $n$ time points, $0 < t_1 < t_2 < \cdots < t_n < T$, within a time span $T > 0$.
We wish ...
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Increase the number of samples when the PDF is invariant
Background:
$$\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$$ is given by Fick's second law, in which $D$ is the diffusion coefficient.
The solution to this equation (given the ...
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Why is the sample variance equal to the average sample size for random processes?
I am learning auto-correlation function for fluorescence correlation spectroscopy (FCS) on fcsXpert.com. The web page says:
For random processes such as diffusion, the average of the square of the ...
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Distribution of the step size of diffusion in 3-dimensional space
I need to find the distribution of the random variable
$$Y=\sqrt{X_1^2+X_2^2+X_3^2}$$
where $X_i\sim{\cal{N}}(0,\sigma^2)$ and $\sigma^2$ is related to diffusion coefficient. All $X_i$s are ...
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How to simulate anomalous diffusion of a 1D point like particle?
I want to simulate 3 types of diffusion processes:
normal diffusion $[\langle x^2(t)\rangle \propto t ]$.
subdiffusion $[\langle x^2(t)\rangle \propto t^\alpha ; \alpha<1 ]$
superdiffusion $[\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Probability distribution of the magnitude of a circular bivariate random variable?
I'm very new to this topic. I have a distribution similar to the picture below but with the center at zero.
As I said, I'm very new to this, but if I understand correctly, if there was no hole in ...
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