Mathematical Foundations of Generative AI · Quiz 2 · Sep 2025

Mathematical Foundations of Generative AI · Quiz 2 · Sep 2025

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Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

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Question 91 MCQ · 3.0 marks

In a Denoising Diffusion Probabilistic Model (DDPM), the sampling process works by running the reverse diffusion steps:

Are these reverse steps in DDPM usually stochastic (i.e., involve random noise at each step) rather than purely deterministic?

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Correct

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Incorrect

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Question 92 MCQ · 3.0 marks

A DDPM is trained with

time steps. If the initial time step

has a very small

(variance), and the final time step

has a very large

, what is the resulting value of the total added noise component

at

and

?

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: Close to

;

: Close to

.

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: Close to

;

: Close to

.

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: Close to

;

: Close to

.

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: Close to

;

: Close to

.

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Question 93 MCQ · 3.0 marks

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The

is fixed because the variance is independent of the data, determined only by the time step

.

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Fixing the variance simplifies the ELBO such that the objective only needs to predict the noise, which implicitly predicts the mean.

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The variance

is not fixed; the U-Net predicts both the mean

and the variance

simultaneously.

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The variance is fixed because the U-Net is designed only to denoise, not to estimate uncertainty.

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Question 95 MSQ · 3.0 marks

In contrast to a standard VAE, a VQ-VAE does NOT typically include which of the following?

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The reparameterization trick (

).

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A reconstruction loss term (like MSE or Cross-Entropy).

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A decoder network.

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A KL Divergence loss term.

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Question 96 NAT · 3.0 marks

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Question 97 MCQ · 3.0 marks

In the standard VAE graphical model, what is the sequence of dependencies that constitutes the generative process (Inference)?

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Input

Decoder

Latent

Prior

Reconstruction

.

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Encoder

Latent

Prior

.

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Prior

Latent

Decoder

Sample

.

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Input

Encoder

Latent

Decoder

Reconstruction

.

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Question 98 MCQ · 3.0 marks

Posterior collapse (where

for all

) is a failure mode in VAEs. Which component of the VAE loss, when overwhelmingly strong, is the primary mathematical driver of this phenomenon?

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The gradient flow from the decoder to the encoder.

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The Reconstruction Loss (expected log-likelihood).

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The mean term,

, of the reparameterization trick.

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The

-weighted KL Divergence term.

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Question 99 MCQ · 4.0 marks

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Question 100 MCQ · 4.0 marks

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6406535902987.

6406535902988.

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Question 101 MCQ · 4.0 marks

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6406535902990.

6406535902991.

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Question 102 MCQ · 4.0 marks

Consider a variance-preserving diffusion process with a variance schedule

, and define

The forward diffusion process is given by

which admits the reparameterization

The reverse process is modeled as

For this linear-Gaussian forward process, what are the correct expressions for the posterior mean and variance of

?

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Question 103 MSQ · 4.0 marks

In a

-VAE, the Evidence Lower Bound (ELBO) is modified as:

Increasing

(i.e.,

) tends to:

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Strengthen disentanglement between latent dimensions.

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Encourage sharper image reconstructions. (in case of image dataset)

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Reduce mutual information between

and

.

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Make the latent posterior

closer to the prior

.

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Question 104 MCQ · 3.0 marks

If the KL term

goes to nearly 0 for all

during training the VAE, what situation might be happening?

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The encoder ignores the input

and outputs something close to the prior for all inputs.

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The encoder perfectly memorizes each input in

.

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