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Durk Kingma is a computer scientist who publishes as Diederik P. Kingma. His personal profile describes research on machine learning and generative models, and records a 2017 doctorate at the University of Amsterdam.^[ref] The institutional thesis front matter gives his full formal name as Diederik Pieter Kingma.^[ref]

Kingma and Max Welling coauthored Auto-Encoding Variational Bayes by Diederik P. Kingma and Max Welling. A variational autoencoder couples a latent-variable model with an approximating posterior distribution that can be optimized through variational inference. Their reparameterization gradients represent a simulated random variable as a differentiable transformation of parameter-independent noise, allowing derivatives through the transformation.^[ref] Kingma also coauthored the Adam paper with Jimmy Lei Ba.^[ref]

An original scalar calculation makes the noise handling concrete. Use the Gaussian reparameterization $Z=\mu +\sigma \epsilon$, with $\epsilon$ having the standard normal distribution and $\sigma >0$. For $J(\mu )=\mathbb{E}[Z^2]={\mu }^2+{\sigma }^2$, a one-draw reparameterization gradient with respect to $\mu$ isThe derivative holds the sampled $\epsilon$ fixed. This pathwise gradient is justified here by direct calculation; a general interchange of derivative and expected value requires differentiation under the integral sign conditions.

Noise coupling matters even for a central finite difference. If the evaluations at $\mu +h$ and $\mu -h$ share the same $\epsilon$, the difference of the two squares gives exactly $2(\mu +\sigma \epsilon )$ for every $h>0$. This is a use of common random numbers. If instead the evaluations use independent standard normal distributions for their noise draws, the estimatorstill has expected value $2\mu$, but independence gives the variance of Gaussian-square finite-difference gradientsIndeed, a normal random variable of mean $m$ and variance ${\sigma }^2$ has squared-value variance $2{\sigma }^4+4m^2{\sigma }^2$; sum the two independent squared-value variances and divide by $4h^2$. Thus shrinking $h$ need not suppress simulation noise.

For chosen $\mu =1$, $\sigma =2$ and $h=0.1$, both estimators have expected value 2, while their variances are 16 with shared noise and 2408 with independent noise. The example is a separate exact quadratic model; its purpose is to explain the role of keeping base noise fixed, not to reproduce a published variational-autoencoder benchmark.

Max Welling coauthored Auto-Encoding Variational Bayes by Diederik P. Kingma and Max Welling with Durk Kingma. Their work combines a learned approximate posterior with a differentiable transformation of parameter-independent noise, permitting variational inference to use a reparameterization gradient. The original preprint was submitted in December 2013; its historical byline uses Diederik P. Kingma.^[ref]

An original scalar calculation illustrates the computational mechanism. Let $Z=\mu +\sigma ϵ$, where $ϵ$ has a standard normal distribution and $\sigma >0$. For the chosen objective $J=\mathbb{E}[Z^2]$,Holding one noise draw fixed while differentiating its squared transformed value instead gives the stochastic estimates $2Z$ and $2Zϵ$. At chosen $\mu =1$, $\sigma =2$ and $ϵ=1$, these are both $6$, while the exact expectation gradients are $2$ and $4$. Averaging over the noise, rather than treating one draw as the expectation, recovers the exact gradients in this example.

This small calculation isolates the differentiable sampling step. A variational autoencoder also specifies a probabilistic model and an evidence lower bound; a differentiable random transformation alone does not supply those components. The contribution is joint work, not a claim that one coauthor alone originated every part of the method.