Questions tagged [diffusion]
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57 questions
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Why does the DDPM noise predictor model require both the image and time step as input?
Title: Why does the DDPM noise predictor model require both the image and time step as input?
Question:
In DDPM (Denoising Diffusion Probabilistic Models), the model predicts noise in the denoising ...
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Why do we need the small-$\beta_t$ ( ≒ Gaussian $q(x_{t-1}\mid x_t)$ ) assumption in diffusion models
In diffusion models, the forward process is
$q(x_t \mid x_{t-1}) = \mathcal{N}\big(x_{t};\sqrt{1-\beta_t} x_{t-1},\beta_t I\big)$, and the reverse model is parameterized as
$p_\theta(x_{t-1}\mid x_t)=\...
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Probability of hitting time and additional time $X+Y$ in a diffusion process
Let $X$ follow an inverse Gaussian distribution, and $Y\mid X$ a Gaussian distribution.
$$X \sim IG\left( \frac{\alpha}{v_X}, \frac{\alpha^2}{2D_X} \right)$$
$$Y_{\text{given $X=x$}} \sim \mathcal N(...
- 95k
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What are the benefits of consistency loss in consistency model distillation?
When training consistency models with distillation, the loss is designed to drive the model to produce similar outputs on two consecutive points of the discretized probability flow ODE trajectory (eq. ...
- 181
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Derive ELBO for Diffusion Models (MHVAE)
I'm trying to derive the ELBO (Evidence Lower Bound) based loss-function used for training Diffusion Models.
The following equation(s) are from arXiv:2208.11970
Eq. 43 is written as follows:
$$
\...
- 240
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39
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Score Matching Algorithim
I've been reading about score matching and I have a very basic question about how one would (naively) implement the algorithm via gradient descent.
Say I have some sort of neural network that that ...
- 155
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Prove DDPM with an optimal noise prediction network has correct posterior
I am reading through the DDPM paper, and I am trying to understand the following.
Imagine that $\epsilon_{\theta}(x_t,t)$ is our noise predictor. Further imagine that it is fully expressive, i.e., $\...
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309
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Deriving the score of a diffusion model under DDIM
I am trying to understand how the linear relationship between the diffusion noise prediction model $\epsilon_\theta(x_t)$ which predicts noise added to a sample and the score function is derived $$\...
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Derivation of expectation with subscript
I am going through the derivation for Denoising Diffusion Probabilistic Models (DDPMs) based on Calvin Luo's Diffusion tutorial, where he finally develops the reconstruction term, the prior matching ...
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231
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How to derive Diffusion Model's reverse conditional probability when it's tractable via conditioning on $x_0$
Can anyone help me with understanding how the $\tilde{\beta}$ and ${\tilde\mu_t{(x_t, x_0)}}$ are derived?
It seems to me that exponential term is a 2nd order polynomial term and it doesn't really ...
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In diffusion models (DDPM), if we predict the total noise, why not just remove the noise in one shot for sampling?
As pointed out by the DDPM paper, we can choose to reparameterize the prediction of the mean to prediction of the total noise "εθ is a function approximator intended to predict ε from x" (...
- 293
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Does probability flow ODE trajectory (in the context of diffusion models) represents a bijective mapping between any distribution to a gaussian?
I have read several papers about diffusion models in the context of deep learning. especially this one
As explained in the paper, by learning the score function (∇log(𝑝𝑡(𝑥)))
,probability flow ode ...
- 121
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334
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Why do we say that we're "predicting" the mean/noise in diffusion models?
In DDPM, ${\tilde\mu}_t$ is the mean of the conditional distribution $q(x_{t-1}|x_t,x_0)$ while the neural network $\mu_\theta$ is modeling a different conditional distribution $p_\theta(x_{t-1}|x_t)$....
- 293
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Why is the forward process referred to as the "ground truth" in diffusion models?
I've seen in many tutorials on diffusion models refer to the distribution of the latent variables induced by the forward process as "ground truth". I wonder why. What we can actually see is ...
- 293
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Why does Variational Inference work?
ELBO is a lower bound, and only matches the true likelihood when the q-distribution/encoder we choose equals to the true posterior distribution. Are there any guarantees that maximizing ELBO indeed ...
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