da5002_2025T3_Q2_NA.pdf
Mathematical Foundations of Generative AI · Quiz 2 · Sep 2025
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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:
[[IMAGE:2d65ea2f8ed9ca96_2_3]]
Are these reverse steps in DDPM usually stochastic (i.e., involve random noise at each step) rather
than purely deterministic?
Correct
Incorrect
A published solution is not available for this question yet.
Question 92 MCQ · 3.0 marks
A DDPM is trained with [[IMAGE:2d65ea2f8ed9ca96_2_4]] time steps. If the initial time step [[IMAGE:2d65ea2f8ed9ca96_2_5]] has a very small [[IMAGE:2d65ea2f8ed9ca96_2_6]]
(variance), and the final time step [[IMAGE:2d65ea2f8ed9ca96_2_7]] has a very large [[IMAGE:2d65ea2f8ed9ca96_2_8]] , what is the resulting value of the
total added noise component [[IMAGE:2d65ea2f8ed9ca96_2_9]] at [[IMAGE:2d65ea2f8ed9ca96_2_10]] and [[IMAGE:2d65ea2f8ed9ca96_2_11]] ?
[[IMAGE:2d65ea2f8ed9ca96_2_12]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_13]] ; [[IMAGE:2d65ea2f8ed9ca96_2_14]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_15]] .
[[IMAGE:2d65ea2f8ed9ca96_2_16]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_17]] ; [[IMAGE:2d65ea2f8ed9ca96_2_18]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_19]] .
[[IMAGE:2d65ea2f8ed9ca96_2_20]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_21]] ; [[IMAGE:2d65ea2f8ed9ca96_2_22]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_23]] .
[[IMAGE:2d65ea2f8ed9ca96_2_24]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_25]] ; [[IMAGE:2d65ea2f8ed9ca96_2_26]] : Close to [[IMAGE:2d65ea2f8ed9ca96_2_27]] .
A published solution is not available for this question yet.
Question 93 MCQ · 3.0 marks
[[IMAGE:2d65ea2f8ed9ca96_3_28]]
The [[IMAGE:2d65ea2f8ed9ca96_3_29]] is fixed because the variance is independent of the data, determined
only by the time step [[IMAGE:2d65ea2f8ed9ca96_3_30]] .
Fixing the variance simplifies the ELBO such that the objective only needs to
predict the noise, which implicitly predicts the mean.
The variance [[IMAGE:2d65ea2f8ed9ca96_3_31]] is not fixed; the U-Net predicts both the mean [[IMAGE:2d65ea2f8ed9ca96_3_32]] and the
variance [[IMAGE:2d65ea2f8ed9ca96_3_33]] simultaneously.
The variance is fixed because the U-Net is designed only to denoise, not to
estimate uncertainty.
A published solution is not available for this question yet.
Question 94 MCQ · 3.0 marks
In a Vector Quantized VAE, the encoder outputs a continuous vector which is then:
Sent directly to the decoder with no change.
Thresholded element-wise at 0.
Replaced by the nearest code vector from a learned codebook.
Sorted in descending order.
A published solution is not available for this question yet.
Question 95 MSQ · 3.0 marks
In contrast to a standard VAE, a VQ-VAE does NOT typically include which of the following?
The reparameterization trick ( [[IMAGE:2d65ea2f8ed9ca96_4_34]] ).
A reconstruction loss term (like MSE or Cross-Entropy).
A decoder network.
A KL Divergence loss term.
A published solution is not available for this question yet.
Question 96 NAT · 3.0 marks
[[IMAGE:2d65ea2f8ed9ca96_4_35]]
A published solution is not available for this question yet.
Question 97 MCQ · 3.0 marks
In the standard VAE graphical model, what is the sequence of dependencies that constitutes the
generative process (Inference)?
Input [[IMAGE:2d65ea2f8ed9ca96_4_36]] Decoder [[IMAGE:2d65ea2f8ed9ca96_4_37]] Latent [[IMAGE:2d65ea2f8ed9ca96_4_38]] Prior [[IMAGE:2d65ea2f8ed9ca96_4_39]] Reconstruction [[IMAGE:2d65ea2f8ed9ca96_4_40]] .
Encoder [[IMAGE:2d65ea2f8ed9ca96_4_41]] Latent [[IMAGE:2d65ea2f8ed9ca96_4_42]] Prior [[IMAGE:2d65ea2f8ed9ca96_4_43]] .
Prior [[IMAGE:2d65ea2f8ed9ca96_5_44]] Latent [[IMAGE:2d65ea2f8ed9ca96_5_45]] Decoder [[IMAGE:2d65ea2f8ed9ca96_5_46]] Sample [[IMAGE:2d65ea2f8ed9ca96_5_47]] .
Input [[IMAGE:2d65ea2f8ed9ca96_5_48]] Encoder [[IMAGE:2d65ea2f8ed9ca96_5_49]] Latent [[IMAGE:2d65ea2f8ed9ca96_5_50]] Decoder [[IMAGE:2d65ea2f8ed9ca96_5_51]] Reconstruction
[[IMAGE:2d65ea2f8ed9ca96_5_52]] .
A published solution is not available for this question yet.
Question 98 MCQ · 3.0 marks
Posterior collapse (where [[IMAGE:2d65ea2f8ed9ca96_5_53]] for all [[IMAGE:2d65ea2f8ed9ca96_5_54]] ) is a failure mode in VAEs. Which component of
the VAE loss, when overwhelmingly strong, is the primary mathematical driver of this
phenomenon?
The gradient flow from the decoder to the encoder.
The Reconstruction Loss (expected log-likelihood).
The mean term, [[IMAGE:2d65ea2f8ed9ca96_5_55]] , of the reparameterization trick.
The [[IMAGE:2d65ea2f8ed9ca96_5_56]] -weighted KL Divergence term.
A published solution is not available for this question yet.
Question 99 MCQ · 4.0 marks
[[IMAGE:2d65ea2f8ed9ca96_6_57]]
[[IMAGE:2d65ea2f8ed9ca96_6_58]]
[[IMAGE:2d65ea2f8ed9ca96_6_59]]
[[IMAGE:2d65ea2f8ed9ca96_6_60]]
[[IMAGE:2d65ea2f8ed9ca96_6_61]]
A published solution is not available for this question yet.
Question 100 MCQ · 4.0 marks
[[IMAGE:2d65ea2f8ed9ca96_6_62]]
[[IMAGE:2d65ea2f8ed9ca96_7_63]]
[[IMAGE:2d65ea2f8ed9ca96_7_64]]
[[IMAGE:2d65ea2f8ed9ca96_7_65]]
[[IMAGE:2d65ea2f8ed9ca96_7_66]]
A published solution is not available for this question yet.
Question 101 MCQ · 4.0 marks
[[IMAGE:2d65ea2f8ed9ca96_7_67]]
[[IMAGE:2d65ea2f8ed9ca96_8_68]]
[[IMAGE:2d65ea2f8ed9ca96_8_69]]
[[IMAGE:2d65ea2f8ed9ca96_8_70]]
[[IMAGE:2d65ea2f8ed9ca96_8_71]]
A published solution is not available for this question yet.
Question 102 MCQ · 4.0 marks
Consider a variance-preserving diffusion process with a variance schedule
[[IMAGE:2d65ea2f8ed9ca96_8_72]] , and define
[[IMAGE:2d65ea2f8ed9ca96_8_73]]
The forward diffusion process is given by
[[IMAGE:2d65ea2f8ed9ca96_8_74]]
which admits the reparameterization
[[IMAGE:2d65ea2f8ed9ca96_8_75]]
The reverse process is modeled as
[[IMAGE:2d65ea2f8ed9ca96_8_76]]
For this linear-Gaussian forward process, what are the correct expressions
for the posterior mean and variance of [[IMAGE:2d65ea2f8ed9ca96_8_77]] ?
[[IMAGE:2d65ea2f8ed9ca96_8_78]]
[[IMAGE:2d65ea2f8ed9ca96_8_79]]
[[IMAGE:2d65ea2f8ed9ca96_8_80]]
[[IMAGE:2d65ea2f8ed9ca96_9_81]]
[[IMAGE:2d65ea2f8ed9ca96_9_82]] [[IMAGE:2d65ea2f8ed9ca96_9_83]]
[[IMAGE:2d65ea2f8ed9ca96_9_84]]
[[IMAGE:2d65ea2f8ed9ca96_9_85]]
A published solution is not available for this question yet.
Question 103 MSQ · 4.0 marks
In a [[IMAGE:2d65ea2f8ed9ca96_9_86]] -VAE, the Evidence Lower Bound (ELBO) is modified as:
[[IMAGE:2d65ea2f8ed9ca96_9_87]]
Increasing [[IMAGE:2d65ea2f8ed9ca96_9_88]] (i.e., [[IMAGE:2d65ea2f8ed9ca96_9_89]] ) tends to:
Strengthen disentanglement between latent dimensions.
Encourage sharper image reconstructions. (in case of image dataset)
Reduce mutual information between [[IMAGE:2d65ea2f8ed9ca96_9_90]] and [[IMAGE:2d65ea2f8ed9ca96_9_91]] .
Make the latent posterior [[IMAGE:2d65ea2f8ed9ca96_9_92]] closer to the prior [[IMAGE:2d65ea2f8ed9ca96_9_93]] .
A published solution is not available for this question yet.
Question 104 MCQ · 3.0 marks
If the KL term [[IMAGE:2d65ea2f8ed9ca96_9_94]] goes to nearly 0 for all [[IMAGE:2d65ea2f8ed9ca96_9_95]] during training the VAE, what situation
might be happening?
The encoder ignores the input [[IMAGE:2d65ea2f8ed9ca96_9_96]] and outputs something close to the prior for
all inputs.
The encoder perfectly memorizes each input in [[IMAGE:2d65ea2f8ed9ca96_9_97]] .
A published solution is not available for this question yet.