Diffusion model - Revision history

Rice at 23:08, 5 July 2024

2024-07-05T23:08:24Z

← Older revision		Revision as of 23:08, 5 July 2024
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	==== Noising process ====		==== Noising process ====
	Thus, the entire noise added at time step ''T'' is defined to be <math>q(x_{1:T} \|x_0)=\prod^T_{t=i}q(x_t\|x_{t-1})</math>, coming form probability.		Thus, the entire noise added at time step ''T'' is defined to be <math>q(x_{1:T} \|x_0)=\prod^T_{t=i}q(x_t\|x_{t-1})</math>, coming form probability.

			With the derivation in source 1, we can simplify it to a single equation instead of an iterative process, significantly speeding up the algorithm.

	= Sources =		= Sources =

	* https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models		# https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models
	* [https://www.youtube.com/watch?v=fbLgFrlTnGU&t=75s https://www.youtube.com/watch?v=fbLgFrlTnGU]		# [https://www.youtube.com/watch?v=fbLgFrlTnGU&t=75s https://www.youtube.com/watch?v=fbLgFrlTnGU]

	[[Category:Computer Science]]		[[Category:Computer Science]]
	[[Category:Machine Learning]]		[[Category:Machine Learning]]

Rice: /* Principle */

2024-07-05T23:06:48Z

Principle

← Older revision		Revision as of 23:06, 5 July 2024
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	Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.		Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.

			==== Schedule ====
			''Beta t'' is the hyperparameter called ''schedule''. It increases w.r.t. time step ''t'' and controls the variance of the distribution during the forward process. It is a value ranging from 0 to 1, and as a result, it brings the mean of the gaussian closer to 0 and the variance closer to ''I'', which is the goal of the forward process.

			We want a small schedule such that learning how to undo it isn't too difficult.

			==== Noising process ====
			Thus, the entire noise added at time step ''T'' is defined to be <math>q(x_{1:T} \|x_0)=\prod^T_{t=i}q(x_t\|x_{t-1})</math>, coming form probability.

	= Sources =		= Sources =

	* https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models		* https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models
			* [https://www.youtube.com/watch?v=fbLgFrlTnGU&t=75s https://www.youtube.com/watch?v=fbLgFrlTnGU]

	[[Category:Computer Science]]		[[Category:Computer Science]]
	[[Category:Machine Learning]]		[[Category:Machine Learning]]

Rice: /* Forward diffusion */

2024-07-05T00:37:48Z

Forward diffusion

← Older revision		Revision as of 00:37, 5 July 2024
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	=== Forward diffusion ===		=== Forward diffusion ===
	Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a [[multivariate normal distribution]], the square root is the mean, and the last one being the variance.		Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=\mathcal{N}(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a [[multivariate normal distribution]], the square root is the mean, and the last one being the variance.

	Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.		Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.

Rice: /* Forward diffusion */

2024-07-05T00:15:03Z

Forward diffusion

← Older revision		Revision as of 00:15, 5 July 2024
Line 7:		Line 7:

	=== Forward diffusion ===		=== Forward diffusion ===
	Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a normal distribution, the square root is the mean, and the last one being the variance.		Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a [[multivariate normal distribution]], the square root is the mean, and the last one being the variance.

	Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.		Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.

Rice: /* Forward diffusion */

2024-07-04T23:38:05Z

Forward diffusion

← Older revision		Revision as of 23:38, 4 July 2024
Line 9:		Line 9:
	Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a normal distribution, the square root is the mean, and the last one being the variance.		Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a normal distribution, the square root is the mean, and the last one being the variance.

	Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule.		Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule. The image starts with a non-random distribution, and through this process we destroy that distribution into noise. In real scenarios, the noise is not added iteratively, but this is the principle.

	= Sources =		= Sources =

Rice: /* Forward diffusion */

2024-07-04T23:25:00Z

Forward diffusion

← Older revision		Revision as of 23:25, 4 July 2024
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	=== Forward diffusion ===		=== Forward diffusion ===
	Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}, \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a normal distribution, the square root is the mean, and the last one being the variance.		Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}x_{t-1} , \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a normal distribution, the square root is the mean, and the last one being the variance.

			Explained more textually, the process generates a probability distribution of the current step (''x<sub>t</sub>'') given the last step. The distribution is normal, with randomness injected by a schedule.

	= Sources =		= Sources =

Rice: /* Principle */

2024-07-04T23:19:05Z

Principle

← Older revision		Revision as of 23:19, 4 July 2024
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	=== Forward diffusion ===		=== Forward diffusion ===
	Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}, \beta_tI)</math>, where ~~''q'' is the process, ''N'' is a normal distribution,~~ ''x<sub>t</sub>'' is the process output at step ''t'', the square root is the mean, and the last one being the variance.		Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}, \beta_tI)</math>, where ''x<sub>t</sub>'' is the process output at step ''t'', ''q'' is a distribution at the current step depending on the previous step, ''N'' is a normal distribution, the square root is the mean, and the last one being the variance.

	= Sources =		= Sources =

Rice at 23:15, 4 July 2024

2024-07-04T23:15:40Z

← Older revision		Revision as of 23:15, 4 July 2024
Line 7:		Line 7:

	=== Forward diffusion ===		=== Forward diffusion ===
	Mathematically, forward diffusion is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}, \beta_tI)</math>, where ''q'' is the ~~forward diffusion~~ process,		Mathematically, each step of the forward diffusion process is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}, \beta_tI)</math>, where ''q'' is the process, ''N'' is a normal distribution, ''x<sub>t</sub>'' is the process output at step ''t'', the square root is the mean, and the last one being the variance.

	= Sources =		= Sources =

Rice at 22:59, 4 July 2024

2024-07-04T22:59:45Z

← Older revision		Revision as of 22:59, 4 July 2024
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			In a nutshell, '''diffusion models''' work by making something more random/noisy, and through the process finding the inverse, which is making noisy things less random, thus generating data.

			Diffusion models are frequently used for computer vision tasks such as text-to-image. This page will focus exclusively on that use case.

			== Principle ==
			More specifically, diffusion models consists of two steps: ''forward'' ''diffusion'', which turns an image into noise, and ''backward diffusion'', which turns noise back into an image.

			=== Forward diffusion ===
			Mathematically, forward diffusion is defined as <math>q(x_t\|x_{t-1})=N(x_t, \sqrt{1-\beta_t}, \beta_tI)</math>, where ''q'' is the forward diffusion process,

	= Sources =		= Sources =

Rice: Created page with "= Sources = * https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models Category:Computer Science Category:Machine Learning"

2024-07-04T22:35:10Z

Created page with "= Sources = * https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models Category:Computer Science Category:Machine Learning"

New page

= Sources =

* https://erdem.pl/2023/11/step-by-step-visual-introduction-to-diffusion-models

[[Category:Computer Science]]
[[Category:Machine Learning]]