7
votes
Accepted
Reconciling Langevin MC methods as one-step HMC versus as diffusion or brownian motion
The easiest way to understand why Langevin dynamics targets the "correct distribution" is to look at the corresponding Fokker-Planck equation.
Let me be more precise. Let us assume that our target ...
- 271
4
votes
Accepted
Does Langevin MCMC with decreasing step size require Metropolis-Hastings?
You wrote a very weird expression for Langevin MCMC (which is a special case of Diffusion Markov Chain Monte Carlo). On the right hand side you only have gradients of the prior and the likelihood at ...
- 18.4k
1
vote
How to calculate the score of a new datapoint by a score based diffusion model(song & ermon, 2019)?
My interpretation of your question is how the calculation of the score function is related to diffusion models. A possible derivation therefore involves employing Tweedie's formula, defined as
$\...
- 376
1
vote
Accepted
Why convolving a function with a Gaussian kernel is the same as adding a Gaussian noise to the input?
What is true is the following: if $\epsilon \sim \mathcal{N}(0,\sigma^2)$, then $\mathbb{E}[p(x+\epsilon)] = (p * \omega)(x)$, if $\omega$ is the density of $\mathcal{N}(0,\sigma^2)$. In fact, this ...
- 262
1
vote
What is the exact role of model $p_\theta$ in Diffusion models for the reverse process?
I understand that indeed we don't have any prior knowledge of $q(x_{t−1})$ or $q(x_t)$ since this would mean already having the distribution we are trying to estimate. Is this correct?
Yes, I think ...
- 505
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