A Visual Guide to How Diffusion Models Work

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A Visual Guide to How Diffusion Models Work

This article is aimed at those who want to understand exactly how Diffusion Models work, with no prior knowledge expected. I’ve tried to use illustrations wherever possible to provide visual intuitions on each part of these models. I’ve kept mathematical notation and equations to a minimum, and where they are necessary I’ve tried to define […]

Intro

I’ve framed this article around three main questions:

What exactly is it that diffusion models learn?
How and why do diffusion models work?
Once you’ve trained a model, how do you get useful stuff out of it?

The examples will be based on the glyffuser, a minimal text-to-image diffusion model that I previously implemented and wrote about. The architecture of this model is a standard text-to-image denoising diffusion model without any bells or whistles. It was trained to generate pictures of new “Chinese” glyphs from English definitions. Have a look at the picture below — even if you’re not familiar with Chinese writing, I hope you’ll agree that the generated glyphs look pretty similar to the real ones!

Random examples of glyffuser training data (left) and generated data (right).

What exactly is it that diffusion models learn?

Generative Ai models are often said to take a big pile of data and “learn” it. For text-to-image diffusion models, the data takes the form of pairs of images and descriptive text. But what exactly is it that we want the model to learn? First, let’s forget about the text for a moment and concentrate on what we are trying to generate: the images.

Probability distributions

Broadly, we can say that we want a generative AI model to learn the underlying probability distribution of the data. What does this mean? Consider the one-dimensional normal (Gaussian) distribution below, commonly written 𝒩(μ,σ²) and parameterized with mean μ = 0 and variance σ² = 1. The black curve below shows the probability density function. We can sample from it: drawing values such that over a large number of samples, the set of values reflects the underlying distribution. These days, we can simply write something like x = random.gauss(0, 1) in Python to sample from the standard normal distribution, although the computational sampling process itself is non-trivial!

Values sampled from an underlying distribution (here, the standard normal 𝒩(0,1)) can then be used to estimate the parameters of that distribution.

We could think of a set of numbers sampled from the above normal distribution as a simple dataset, like that shown as the orange histogram above. In this particular case, we can calculate the parameters of the underlying distribution using maximum likelihood estimation, i.e. by working out the mean and variance. The normal distribution estimated from the samples is shown by the dotted line above. To take some liberties with terminology, you might consider this as a simple example of “learning” an underlying probability distribution. We can also say that here we explicitly learnt the distribution, in contrast with the implicit methods that diffusion models use.

Conceptually, this is all that generative AI is doing — learning a distribution, then sampling from that distribution!

Data representations

What, then, does the underlying probability distribution of a more complex dataset look like, such as that of the image dataset we want to use to train our diffusion model?

First, we need to know what the representation of the data is. Generally, a machine learning (ML) model requires data inputs with a consistent representation, i.e. format. For the example above, it was simply numbers (scalars). For images, this representation is commonly a fixed-length vector.

The image dataset used for the glyffuser model is ~21,000 pictures of Chinese glyphs. The images are all the same size, 128 × 128 = 16384 pixels, and greyscale (single-channel color). Thus an obvious choice for the representation is a vector x of length 16384, where each element corresponds to the color of one pixel: x = (x₁,x₂,…,x₁₆₃₈₄). We can call the domain of all possible images for our dataset “pixel space”.

An example glyph with pixel values labelled (downsampled to 32 × 32 pixels for readability).

Dataset visualization

We make the assumption that our individual data samples, x, are actually sampled from an underlying probability distribution, q(x), in pixel space, much as the samples from our first example were sampled from an underlying normal distribution in 1-dimensional space. Note: the notation x ∼ q(x) is commonly used to mean: “the random variable x sampled from the probability distribution q(x).”

This distribution is clearly much more complex than a Gaussian and cannot be easily parameterized — we need to learn it with a ML model, which we’ll discuss later. First, let’s try to visualize the distribution to gain a better intution.

As humans find it difficult to see in more than 3 dimensions, we need to reduce the dimensionality of our data. A small digression on why this works: the manifold hypothesis posits that natural datasets lie on lower dimensional manifolds embedded in a higher dimensional space — think of a line embedded in a 2-D plane, or a plane embedded in 3-D space. We can use a dimensionality reduction technique such as UMAP to project our dataset from 16384 to 2 dimensions. The 2-D projection retains a lot of structure, consistent with the idea that our data lie on a lower dimensional manifold embedded in pixel space. In our UMAP, we see two large clusters corresponding to characters in which the components are arranged either horizontally (e.g. 明) or vertically (e.g. 草). An interactive version of the plot below with popups on each datapoint is linked here.

Click here for an interactive version of this plot.

Let’s now use this low-dimensional UMAP dataset as a visual shorthand for our high-dimensional dataset. Remember, we assume that these individual points have been sampled from a continuous underlying probability distribution q(x). To get a sense of what this distribution might look like, we can apply a KDE (kernel density estimation) over the UMAP dataset. (Note: this is just an approximation for visualization purposes.)

This gives a sense of what q(x) should look like: clusters of glyphs correspond to high-probability regions of the distribution. The true q(x) lies in 16384 dimensions — this is the distribution we want to learn with our diffusion model.

We showed that for a simple distribution such as the 1-D Gaussian, we could calculate the parameters (mean and variance) from our data. However, for complex distributions such as images, we need to call on ML methods. Moreover, what we will find is that for diffusion models in practice, rather than parameterizing the distribution directly, they learn it implicitly through the process of learning how to transform noise into data over many steps.

Takeaway

The aim of generative AI such as diffusion models is to learn the complex probability distributions underlying their training data and then sample from these distributions.

How and why do diffusion models work?

Diffusion models have recently come into the spotlight as a particularly effective method for learning these probability distributions. They generate convincing images by starting from pure noise and gradually refining it. To whet your interest, have a look at the animation below that shows the denoising process generating 16 samples.

In this section we’ll only talk about the mechanics of how these models work but if you’re interested in how they arose from the broader context of generative models, have a look at the further reading section below.

What is “noise”?

Let’s first precisely define noise, since the term is thrown around a lot in the context of diffusion. In particular, we are talking about Gaussian noise: consider the samples we talked about in the section about probability distributions. You could think of each sample as an image of a single pixel of noise. An image that is “pure Gaussian noise”, then, is one in which each pixel value is sampled from an independent standard Gaussian distribution, 𝒩(0,1). For a pure noise image in the domain of our glyph dataset, this would be noise drawn from 16384 separate Gaussian distributions. You can see this in the previous animation. One thing to keep in mind is that we can choose the means of these noise distributions, i.e. center them, on specific values — the pixel values of an image, for instance.

For convenience, you’ll often find the noise distributions for image datasets written as a single multivariate distribution 𝒩(0,I) where I is the identity matrix, a covariance matrix with all diagonal entries equal to 1 and zeroes elsewhere. This is simply a compact notation for a set of multiple independent Gaussians — i.e. there are no correlations between the noise on different pixels. In the basic implementations of diffusion models, only uncorrelated (a.k.a. “isotropic”) noise is used. This article contains an excellent interactive introduction on multivariate Gaussians.

Diffusion process overview

Below is an adaptation of the somewhat-famous diagram from Ho et al.’s seminal paper “Denoising Diffusion Probabilistic Models” which gives an overview of the whole diffusion process:

Diagram of the diffusion process adapted from Ho *et al*. 2020. The glyph 锂, meaning “lithium”, is used as a representative sample from the dataset.

I found that there was a lot to unpack in this diagram and simply understanding what each component meant was very helpful, so let’s go through it and define everything step by step.

We previously used x ∼ q(x) to refer to our data. Here, we’ve added a subscript, xₜ, to denote timestep t indicating how many steps of “noising” have taken place. We refer to the samples noised a given timestep as x ∼ q(xₜ). x₀ is clean data and xₜ (t = T) ∼ 𝒩(0,1) is pure noise.

We define a forward diffusion process whereby we corrupt samples with noise. This process is described by the distribution q(xₜ|xₜ₋₁). If we could access the hypothetical reverse process q(xₜ₋₁|xₜ), we could generate samples from noise. As we cannot access it directly because we would need to know x₀, we use ML to learn the parameters, θ, of a model of this process, 𝑝θ(𝑥ₜ₋₁∣𝑥ₜ). (That should be p subscript θ but medium cannot render it.)

In the following sections we go into detail on how the forward and reverse diffusion processes work.

Forward diffusion, or “noising”

Used as a verb, “noising” an image refers to applying a transformation that moves it towards pure noise by scaling down its pixel values toward 0 while adding proportional Gaussian noise. Mathematically, this transformation is a multivariate Gaussian distribution centered on the pixel values of the preceding image.

In the forward diffusion process, this noising distribution is written as q(xₜ|xₜ₋₁) where the vertical bar symbol “|” is read as “given” or “conditional on”, to indicate the pixel means are passed forward from q(xₜ₋₁) At t = T where T is a large number (commonly 1000) we aim to end up with images of pure noise (which, somewhat confusingly, is also a Gaussian distribution, as discussed previously).

The marginal distributions q(xₜ) represent the distributions that have accumulated the effects of all the previous noising steps (marginalization refers to integration over all possible conditions, which recovers the unconditioned distribution).

Since the conditional distributions are Gaussian, what about their variances? They are determined by a variance schedule that maps timesteps to variance values. Initially, an empirically determined schedule of linearly increasing values from 0.0001 to 0.02 over 1000 steps was presented in Ho et al. Later research by Nichol & Dhariwal suggested an improved cosine schedule. They state that a schedule is most effective when the rate of information destruction through noising is relatively even per step throughout the whole noising process.

Forward diffusion intuition

As we encounter Gaussian distributions both as pure noise q(xₜ, t = T) and as the noising distribution q(xₜ|xₜ₋₁), I’ll try to draw the distinction by giving a visual intuition of the distribution for a single noising step, q(x₁∣x₀), for some arbitrary, structured 2-dimensional data:

Each noising step q(xₜ|xₜ₋₁) is a Gaussian distribution conditioned on the previous step.

The distribution q(x₁∣x₀) is Gaussian, centered around each point in x₀, shown in blue. Several example points x₀⁽ⁱ⁾ are picked to illustrate this, with q(x₁∣x₀ = x₀⁽ⁱ⁾) shown in orange.

In practice, the main usage of these distributions is to generate specific instances of noised samples for training (discussed further below). We can calculate the parameters of the noising distributions at any timestep t directly from the variance schedule, as the chain of Gaussians is itself also Gaussian. This is very convenient, as we don’t need to perform noising sequentially—for any given starting data x₀⁽ⁱ⁾, we can calculate the noised sample xₜ⁽ⁱ⁾ by sampling from q(xₜ∣x₀ = x₀⁽ⁱ⁾) directly.

Forward diffusion visualization

Let’s now return to our glyph dataset (once again using the UMAP visualization as a visual shorthand). The top row of the figure below shows our dataset sampled from distributions noised to various timesteps: xₜ ∼ q(xₜ). As we increase the number of noising steps, you can see that the dataset begins to resemble pure Gaussian noise. The bottom row visualizes the underlying probability distribution q(xₜ).

The dataset xₜ (above) sampled from its probability distribution q(xₜ) (below) at different noising timesteps.

Reverse diffusion overview

It follows that if we knew the reverse distributions q(xₜ₋₁∣xₜ), we could repeatedly subtract a small amount of noise, starting from a pure noise sample xₜ at t = T to arrive at a data sample x₀ ∼ q(x₀). In practice, however, we cannot access these distributions without knowing x₀ beforehand. Intuitively, it’s easy to make a known image much noisier, but given a very noisy image, it’s much harder to guess what the original image was.

So what are we to do? Since we have a large amount of data, we can train an ML model to accurately guess the original image that any given noisy image came from. Specifically, we learn the parameters θ of an ML model that approximates the reverse noising distributions, pθ(xₜ₋₁ ∣ xₜ) for t = 0, …, T. In practice, this is embodied in a single noise prediction model trained over many different samples and timesteps. This allows it to denoise any given input, as shown in the figure below.

The ML model predicts added noise at any given timestep t.

Next, let’s go over how this noise prediction model is implemented and trained in practice.

How the model is implemented

First, we define the ML model — generally a deep neural network of some sort — that will act as our noise prediction model. This is what does the heavy lifting! In practice, any ML model that inputs and outputs data of the correct size can be used; the U-net, an architecture particularly suited to learning images, is what we use here and frequently chosen in practice. More recent models also use vision transformers.

We use the U-net architecture (Ronneberger *et al*. 2015) for our ML noise prediction model. We train the model by minimizing the difference between predicted and actual noise.

Then we run the training loop depicted in the figure above:

We take a random image from our dataset and noise it to a random timestep tt. (In practice, we speed things up by doing many examples in parallel!)
We feed the noised image into the ML model and train it to predict the (known to us) noise in the image. We also perform timestep conditioning by feeding the model a timestep embedding, a high-dimensional unique representation of the timestep, so that the model can distinguish between timesteps. This can be a vector the same size as our image directly added to the input (see here for a discussion of how this is implemented).
The model “learns” by minimizing the value of a loss function, some measure of the difference between the predicted and actual noise. The mean square error (the mean of the squares of the pixel-wise difference between the predicted and actual noise) is used in our case.
Repeat until the model is well trained.

Note: A neural network is essentially a function with a huge number of parameters (on the order of 10⁶ for the glyffuser). Neural network ML models are trained by iteratively updating their parameters using backpropagation to minimize a given loss function over many training data examples. This is an excellent introduction. These parameters effectively store the network’s “knowledge”.

A noise prediction model trained in this way eventually sees many different combinations of timesteps and data examples. The glyffuser, for example, was trained over 100 epochs (runs through the whole data set), so it saw around 2 million data samples. Through this process, the model implicity learns the reverse diffusion distributions over the entire dataset at all different timesteps. This allows the model to sample the underlying distribution q(x₀) by stepwise denoising starting from pure noise. Put another way, given an image noised to any given level, the model can predict how to reduce the noise based on its guess of what the original image. By doing this repeatedly, updating its guess of the original image each time, the model can transform any noise to a sample that lies in a high-probability region of the underlying data distribution.

Reverse diffusion in practice

We can now revisit this video of the glyffuser denoising process. Recall a large number of steps from sample to noise e.g. T = 1000 is used during training to make the noise-to-sample trajectory very easy for the model to learn, as changes between steps will be small. Does that mean we need to run 1000 denoising steps every time we want to generate a sample?

Luckily, this is not the case. Essentially, we can run the single-step noise prediction but then rescale it to any given step, although it might not be very good if the gap is too large! This allows us to approximate the full sampling trajectory with fewer steps. The video above uses 120 steps, for instance (most implementations will allow the user to set the number of sampling steps).

Recall that predicting the noise at a given step is equivalent to predicting the original image x₀, and that we can access the equation for any noised image deterministically using only the variance schedule and x₀. Thus, we can calculate xₜ₋ₖ based on any denoising step. The closer the steps are, the better the approximation will be.

Too few steps, however, and the results become worse as the steps become too large for the model to effectively approximate the denoising trajectory. If we only use 5 sampling steps, for example, the sampled characters don’t look very convincing at all:

There is then a whole literature on more advanced sampling methods beyond what we’ve discussed so far, allowing effective sampling with much fewer steps. These often reframe the sampling as a differential equation to be solved deterministically, giving an eerie quality to the sampling videos — I’ve included one at the end if you’re interested. In production-level models, these are usually preferred over the simple method discussed here, but the basic principle of deducing the noise-to-sample trajectory is the same. A full discussion is beyond the scope of this article but see e.g. this paper and its corresponding implementation in the Hugging Face diffusers library for more information.

Alternative intuition from score function

To me, it was still not 100% clear why training the model on noise prediction generalises so well. I found that an alternative interpretation of diffusion models known as “score-based modeling” filled some of the gaps in intuition (for more information, refer to Yang Song’s definitive article on the topic.)

The dataset xₜ sampled from its probability distribution q(xₜ) at different noising timesteps; below, we add the score function ∇ₓ log q(xₜ).

I try to give a visual intuition in the bottom row of the figure above: essentially, learning the noise in our diffusion model is equivalent (to a constant factor) to learning the score function, which is the gradient of the log of the probability distribution: ∇ₓ log q(x). As a gradient, the score function represents a vector field with vectors pointing towards the regions of highest probability density. Subtracting the noise at each step is then equivalent to moving following the directions in this vector field towards regions of high probability density.

As long as there is some signal, the score function effectively guides sampling, but in regions of low probability it tends towards zero as there is little to no gradient to follow. Using many steps to cover different noise levels allows us to avoid this, as we smear out the gradient field at high noise levels, allowing sampling to converge even if we start from low probability density regions of the distribution. The figure shows that as the noise level is increased, more of the domain is covered by the score function vector field.

Summary

The aim of diffusion models is learn the underlying probability distribution of a dataset and then be able to sample from it. This requires forward and reverse diffusion (noising) processes.
The forward noising process takes samples from our dataset and gradually adds Gaussian noise (pushes them off the data manifold). This forward process is computationally efficient because any level of noise can be added in closed form a single step.
The reverse noising process is challenging because we need to predict how to remove the noise at each step without knowing the original data point in advance. We train a ML model to do this by giving it many examples of data noised at different timesteps.
Using very small steps in the forward noising process makes it easier for the model to learn to reverse these steps, as the changes are small.
By applying the reverse noising process iteratively, the model refines noisy samples step by step, eventually producing a realistic data point (one that lies on the data manifold).

Takeaway

Diffusion models are a powerful framework for learning complex data distributions. The distributions are learnt implicitly by modelling a sequential denoising process. This process can then be used to generate samples similar to those in the training distribution.

Once you’ve trained a model, how do you get useful stuff out of it?

Earlier uses of generative AI such as “This Person Does Not Exist” (ca. 2019) made waves simply because it was the first time most people had seen AI-generated photorealistic human faces. A generative adversarial network or “GAN” was used in that case, but the principle remains the same: the model implicitly learnt a underlying data distribution — in that case, human faces — then sampled from it. So far, our glyffuser model does a similar thing: it samples randomly from the distribution of Chinese glyphs.

The question then arises: can we do something more useful than just sample randomly? You’ve likely already encountered text-to-image models such as Dall-E. They are able to incorporate extra meaning from text prompts into the diffusion process — this in known as conditioning. Likewise, diffusion models for scientific scientific applications like protein (e.g. Chroma, RFdiffusion, AlphaFold3) or inorganic crystal structure generation (e.g. MatterGen) become much more useful if can be conditioned to generate samples with desirable properties such as a specific symmetry, bulk modulus, or band gap.

Conditional distributions

We can consider conditioning as a way to guide the diffusion sampling process towards particular regions of our probability distribution. We mentioned conditional distributions in the context of forward diffusion. Below we show how conditioning can be thought of as reshaping a base distribution.

A simple example of a joint probability distribution p(x, y), shown as a contour map, along with its two marginal 1-D probability distributions, p(x) and p(y). The highest points of p(x, y) are at (x₁, y₁) and (x₂, y₂). The conditional distributions p(x∣y = y₁) and p(x∣y = y₂) are shown overlaid on the main plot.

Consider the figure above. Think of p(x) as a distribution we want to sample from (i.e., the images) and p(y) as conditioning information (i.e., the text dataset). These are the marginal distributions of a joint distribution p(x, y). Integrating p(x, y) over y recovers p(x), and vice versa.

Sampling from p(x), we are equally likely to get x₁ or x₂. However, we can condition on p(y = y₁) to obtain p(x∣y = y₁). You can think of this as taking a slice through p(x, y) at a given value of y. In this conditioned distribution, we are much more likely to sample at x₁ than x₂.

In practice, in order to condition on a text dataset, we need to convert the text into a numerical form. We can do this using large language model (LLM) embeddings that can be injected into the noise prediction model during training.

Embedding text with an LLM

In the glyffuser, our conditioning information is in the form of English text definitions. We have two requirements: 1) ML models prefer fixed-length vectors as input. 2) The numerical representation of our text must understand context — if we have the words “lithium” and “element” nearby, the meaning of “element” should be understood as “chemical element” rather than “heating element”. Both of these requirements can be met by using a pre-trained LLM.

The diagram below shows how an LLM converts text into fixed-length vectors. The text is first tokenized (LLMs break text into tokens, small chunks of characters, as their basic unit of interaction). Each token is converted into a base embedding, which is a fixed-length vector of the size of the LLM input. These vectors are then passed through the pre-trained LLM (here we use the encoder portion of Google’s T5 model), where they are imbued with additional contextual meaning. We end up with a array of n vectors of the same length d, i.e. a (n, d) sized tensor.

We can convert text to a numerical embedding imbued with contextual meaning using a pre-trained LLM.

Note: in some models, notably Dall-E, additional image-text alignment is performed using contrastive pretraining. Imagen seems to show that we can get away without doing this.

Training the diffusion model with text conditioning

The exact method that this embedding vector is injected into the model can vary. In Google’s Imagen model, for example, the embedding tensor is pooled (combined into a single vector in the embedding dimension) and added into the data as it passes through the noise prediction model; it is also included in a different way using cross-attention (a method of learning contextual information between sequences of tokens, most famously used in the transformer models that form the basis of LLMs like ChatGPT).

Conditioning information can be added *via* multiple different methods but the training loss remains the same.

In the glyffuser, we only use cross-attention to introduce this conditioning information. While a significant architectural change is required to introduce this additional information into the model, the loss function for our noise prediction model remains exactly the same.

Testing the conditioned diffusion model

Let’s do a simple test of the fully trained conditioned diffusion model. In the figure below, we try to denoise in a single step with the text prompt “Gold”. As touched upon in our interactive UMAP, Chinese characters often contain components known as radicals which can convey sound (phonetic radicals) or meaning (semantic radicals). A common semantic radical is derived from the character meaning “gold”, “金”, and is used in characters that are in some broad sense associated with gold or metals.

Even with a single sampling step, conditioning guides denoising towards the relevant regions of the probability distribution.

The figure shows that even though a single step is insufficient to approximate the denoising trajectory very well, we have moved into a region of our probability distribution with the “金” radical. This indicates that the text prompt is effectively guiding our sampling towards a region of the glyph probability distribution related to the meaning of the prompt. The animation below shows a 120 step denoising sequence for the same prompt, “Gold”. You can see that every generated glyph has either the 釒 or 钅 radical (the same radical in traditional and simplified Chinese, respectively).

Takeaway

Conditioning enables us to sample meaningful outputs from diffusion models.

Further remarks

I found that with the help of tutorials and existing libraries, it was possible to implement a working diffusion model despite not having a full understanding of what was going on under the hood. I think this is a good way to start learning and highly recommend Hugging Face’s tutorial on training a simple diffusion model using their diffusers Python library (which now includes my small bugfix!).

I’ve omitted some topics that are crucial to how production-grade diffusion models function, but are unnecessary for core understanding. One is the question of how to generate high resolution images. In our example, we did everything in pixel space, but this becomes very computationally expensive for large images. The general approach is to perform diffusion in a smaller space, then upscale it in a separate step. Methods include latent diffusion (used in Stable Diffusion) and cascaded super-resolution models (used in Imagen). Another topic is classifier-free guidance, a very elegant method for boosting the conditioning effect to give much better prompt adherence. I show the implementation in my previous post on the glyffuser and highly recommend this article if you want to learn more.

Fun extras

Diffusion sampling using the DPMSolverSDEScheduler developed by Katherine Crowson and implemented in Hugging Face diffusers—note the smooth transition from noise to data.

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@import url(‘https://fonts.googleapis.com/css2?family=Inter:[email protected]&display=swap’); a { color: var(–color-primary-main); } .ebm-page__main h1, .ebm-page__main h2, .ebm-page__main h3, .ebm-page__main h4, .ebm-page__main h5, .ebm-page__main h6 { font-family: Inter; } body { line-height: 150%; letter-spacing: 0.025em; font-family: Inter; } button, .ebm-button-wrapper { font-family: Inter; } .label-style { text-transform: uppercase; color: var(–color-grey); font-weight: 600; font-size: 0.75rem; } .caption-style { font-size: 0.75rem; opacity: .6; } #onetrust-pc-sdk [id*=btn-handler], #onetrust-pc-sdk [class*=btn-handler] { background-color: #c19a06 !important; border-color: #c19a06 !important; } #onetrust-policy a, #onetrust-pc-sdk a, #ot-pc-content a { color: #c19a06 !important; } #onetrust-consent-sdk #onetrust-pc-sdk .ot-active-menu { border-color: #c19a06 !important; } #onetrust-consent-sdk #onetrust-accept-btn-handler, #onetrust-banner-sdk #onetrust-reject-all-handler, #onetrust-consent-sdk #onetrust-pc-btn-handler.cookie-setting-link { background-color: #c19a06 !important; border-color: #c19a06 !important; } #onetrust-consent-sdk .onetrust-pc-btn-handler { color: #c19a06 !important; border-color: #c19a06 !important; } In this Insights episode of the Oil & Gas Journal ReEnterprised podcast, Head of Content Chris Smith updates the evolving situation in Venezuela as the industry attempts to navigate the best path forward while the two governments continue to hammer out the details. The discussion centers on the new legal frameworks being established in both countries within the context of fraught relations stretching back for decades. Want to hear more? Listen in on a January episode highlighting industry’s initial take following the removal of Nicholas Maduro from power. References Politico podcast Monaldi Substack Baker webinar Washington, Caracas open Venezuela to allow more oil sales

Eni makes Calao South discovery offshore Ivory Coast

@import url(‘https://fonts.googleapis.com/css2?family=Inter:[email protected]&display=swap’); a { color: var(–color-primary-main); } .ebm-page__main h1, .ebm-page__main h2, .ebm-page__main h3, .ebm-page__main h4, .ebm-page__main h5, .ebm-page__main h6 { font-family: Inter; } body { line-height: 150%; letter-spacing: 0.025em; font-family: Inter; } button, .ebm-button-wrapper { font-family: Inter; } .label-style { text-transform: uppercase; color: var(–color-grey); font-weight: 600; font-size: 0.75rem; } .caption-style { font-size: 0.75rem; opacity: .6; } #onetrust-pc-sdk [id*=btn-handler], #onetrust-pc-sdk [class*=btn-handler] { background-color: #c19a06 !important; border-color: #c19a06 !important; } #onetrust-policy a, #onetrust-pc-sdk a, #ot-pc-content a { color: #c19a06 !important; } #onetrust-consent-sdk #onetrust-pc-sdk .ot-active-menu { border-color: #c19a06 !important; } #onetrust-consent-sdk #onetrust-accept-btn-handler, #onetrust-banner-sdk #onetrust-reject-all-handler, #onetrust-consent-sdk #onetrust-pc-btn-handler.cookie-setting-link { background-color: #c19a06 !important; border-color: #c19a06 !important; } #onetrust-consent-sdk .onetrust-pc-btn-handler { color: #c19a06 !important; border-color: #c19a06 !important; } Eni SPA discovered gas and condensate in the Murene South-1X exploration well in Block CI-501, Ivory Coast. The well is the first exploration in the block and was drilled by the Saipem Santorini drilling ship about 8 km southwest of the Murene-1X discovery well in adjacent CI-205 block. The well was drilled to about 5,000 m TD in 2,200 m of water. Extensive data acquisition confirmed a main hydrocarbon bearing interval in high-quality Cenomanian sands with a gross thickness of about 50 m with excellent petrophysical properties, the operator said. Murene South-1X will undergo a full conventional drill stem test (DST) to assess the production capacity of this discovery, named Calao South. Calao South confirms the potential of the Calao channel complex that also includes the Calao discovery. It is the second largest discovery in the country after Baleine, with estimated volumes of up to 5.0 tcf of gas and 450 million bbl of condensate (about 1.4 billion bbl of oil). Eni is operator of Block CI-501 (90%) with partner Petroci Holding (10%).

CFEnergía to supply natural gas to low-carbon methanol plant in Mexico

CFEnergía, a subsidiary of Mexico’s Federal Electricity Commission (CFE), has agreed to supply natural gas to Transition Industries LLC for its Pacifico Mexinol project near Topolobampo, Sinaloa, Mexico. Under the signed agreement, which enables the start of Pacifico Mexinol’s construction phase, CFEnergía will supply about 160 MMcfd of natural gas for an unspecified timeframe noted as “long term,” Transition Industries said in a release Feb. 16. The natural gas—to be sourced from the US and supplied at market prices via existing infrastructure—will be used as “critical input for Mexinol’s production of ultra-low carbon methanol,” the company said. Pacifico Mexinol The $3.3-billion Mexinol project, when it begins operations in late 2029 to early 2030, is expected to be the world’s largest ultra-low carbon chemicals plant with production of about 1.8 million tonnes of blue methanol and 350,000 tonnes of green methanol annually. Supply is aimed at markets in Asia, including Japan, while also boosting the development of the domestic market and the Mexican chemical industry. Mitsubishi Gas Chemical has committed to purchasing about 1 million tonnes/year of methanol from the project, about 50% of the project’s planned production. Transition Industries is jointly developing Pacifico Mexinol with the International Finance Corporation (IFC), a member of the World Bank Group. Last year, the company signed a contingent engineering, procurement, and construction (EPC) contract with the consortium of Samsung E&A Co., Ltd., Grupo Samsung E&A Mexico SA de CV, and Techint Engineering and Construction for the project. MAIRE group’s technology division NextChem, through its subsidiary KT TECH SpA, also signed a basic engineering, critical and proprietary equipment supply agreement with Samsung E&A in connection with its proprietary NX AdWinMethanol®Zero technology supply to the project.

North Atlantic’s Gravenchon refinery scheduled for major turnaround

Canada-based North Atlantic Refining Ltd. France-based subsidiary North Atlantic France SAS is undertaking planned maintenance in March at its North Atlantic Energies-operated 230,000-b/d Notre-Dame-de-Gravenchon refinery in Port-Jérôme-sur-Seine, Normandy. Scheduled to begin on Mar. 3 with the phased shutdown of unidentified units at the refinery, the upcoming turnaround will involve thorough inspections of associated equipment designed for continuous operation, as well as unspecified works to improve energy efficiency, environmental performance, and overall competitiveness of the site, North Atlantic Energies said on Feb. 16. Part of the operator’s routine maintenance program aimed at meeting regulatory requirements to ensure the safety, compliance, and long-term performance of the refinery, North Atlantic Energies said the scheduled turnaround will not interrupt product supplies to customers during the shutdown period. While the company confirmed the phased shutdown of units slated for work during the maintenance event would last for several days, the operator did not reveal a definitive timeline for the entire duration of the turnaround. Further details regarding specific works to be carried out during the major maintenance event were not revealed. The upcoming turnaround will be the first to be executed under North Atlantic Group’s ownership, which completed its purchase of the formerly majority-owned ExxonMobil Corp. refinery and associated petrochemical assets at the site in November 2025.

Azule Energy starts Ndungu full field production offshore Angola

Azule Energy has started full field production from Ndungu, part of the Agogo Integrated West Hub Project (IWH) in the western area of Block 15/06, offshore Angola. Ndungo full field lies about 10 km from the NGOMA FPSO in a water depth of around 1,100 m and comprises seven production wells and four injection wells, with an expected production peak of 60,000 b/d of oil. The National Agency for Petroleum, Gas and Biofuels (ANPG) and Azule Energy noted the full field start-up with first oil of three production wells. The phased integration of IWH, with Ndungu full field producing first via N’goma FPSO and later via Agogo FPSO, is expected to reach a peak output of about 175,000 b/d across the two fields. The fields have combined estimated reserves of about 450 million bbl. The Agogo IWH project is operated by Azule Energy with a 36.84% stake alongside partners Sonangol E&P (36.84%) and Sinopec International (26.32%).

Ovintiv to divest Anadarko assets for $3 billion

In a release Feb. 17, Brendan McCracken, Ovintiv president and chief executive officer, said the company has “built one of the deepest premium inventory positions in our industry in the two most valuable plays in North America, the Permian and the Montney,” and that the Anadarko assets sale “positions [Ovintiv] to deliver superior returns for our shareholders for many years to come.” Ovintiv in 2025 had noted plans to sell the asset to help offset the cost of its acquisition of NuVista Energy Ltd. That $2.7-billion cash and stock deal, which closed earlier this month, added about 930 net 10,000-ft equivalent well locations and about 140,000 net acres (70% undeveloped) in the core of the oil-rich Alberta Montney. Proceeds from the Anadarko assets sale are earmarked for accelerated debt reduction, the company said. Ovintiv’s sale of its Anadarko assets is expected to close early in this year’s second quarter, subject to customary conditions, with an effective date of Jan. 1, 2026.

Vertiv’s AI Infrastructure Surge: Record Orders, Liquid Cooling Expansion, and Grid-Scale Power Reflect Data Center Growth

2) “Units of compute”: OneCore and SmartRun On the earnings call, Albertazzi highlighted Vertiv OneCore, an end-to-end data center solution designed to accelerate “time to token,” scaling in 12.5 MW building blocks; and Vertiv SmartRun, a prefabricated white space infrastructure solution aimed at rapidly accelerating fit-out and readiness. He pointed to collaborations (including Hut 8 and Compass Data Centers) as proof points of adoption, emphasizing that SmartRun can stand alone or plug into OneCore. 3) Cooling evolution: hybrid thermal chains and the “trim cooler” Asked how cooling architectures may change (amid industry chatter about warmer-temperature operations and shifting mixes of chillers, CDUs, and other components) Albertazzi leaned into complexity as a feature, not a bug. He argued heat rejection doesn’t disappear, even if some GPU loads can run at higher temperatures. Instead, the future looks hybrid, with mixed loads and resiliency requirements forcing more nuanced thermal chains. Vertiv’s strategic product anchor here is its “trim cooler” concept: a chiller optimized for higher-temperature operation while retaining flexibility for lower-temperature requirements in the same facility, maximizing free cooling where climate and design allow. And importantly, Albertazzi dismissed the idea that CDUs are going away: “We are pretty sure that CDUs in various shapes and forms are a long-term element of the thermal chain.” 4) Edge densification: CoolPhase Ceiling + CoolPhase Row (Feb. 3) Vertiv also expanded its thermal portfolio for edge and small IT environments with the: Vertiv CoolPhase Ceiling (launching Q2 2026): ceiling-mounted, 3.5 kW to 28 kW, designed to preserve floor space. Vertiv CoolPhase Row (available now in North America) for row-based cooling up to 30 kW (300 mm width) or 40 kW (600 mm width). Vertiv Director of Edge Thermal Michal Podmaka tied the products directly to AI-driven edge densification and management consistency, saying the new systems “integrate seamlessly

Execution, Power, and Public Trust: Rich Miller on 2026’s Data Center Reality and Why He Built Data Center Richness

DCF founder Rich Miller has spent much of his career explaining how the data center industry works. Now, with his latest venture, Data Center Richness, he’s also examining how the industry learns. That thread provided the opening for the latest episode of The DCF Show Podcast, where Miller joined present Data Center Frontier Editor in Chief Matt Vincent and Senior Editor David Chernicoff for a wide-ranging discussion that ultimately landed on a simple conclusion: after two years of unprecedented AI-driven announcements, 2026 will be the year reality asserts itself. Projects will either get built, or they won’t. Power will either materialize, or it won’t. Communities will either accept data center expansion – or they’ll stop it. In other words, the industry is entering its execution phase. Why Data Center Richness Matters Now Miller launched Data Center Richness as both a podcast and a Substack publication, an effort to experiment with formats and better understand how professionals now consume industry information. Podcasts have become a primary way many practitioners follow the business, while YouTube’s discovery advantages increasingly make video versions essential. At the same time, Miller remains committed to written analysis, using Substack as a venue for deeper dives and format experimentation. One example is his weekly newsletter distilling key industry developments into just a handful of essential links rather than overwhelming readers with volume. The approach reflects a broader recognition: the pace of change has accelerated so much that clarity matters more than quantity. The topic of how people learn about data centers isn’t separate from the industry’s trajectory; it’s becoming part of it. Public perception, regulatory scrutiny, and investor expectations are now shaped by how stories are told as much as by how facilities are built. That context sets the stage for the conversation’s core theme. Execution Defines 2026 After

Utah’s 4 GW AI Campus Tests the Limits of Speed-to-Power

Back in September 2025, we examined an ambitious proposal from infrastructure developer Joule Capital Partners – often branding the effort as “Joule Power” – in partnership with Caterpillar. The concept is straightforward but consequential: acquire a vast rural tract in Millard County, Utah, and pair an AI-focused data center campus with large-scale, on-site “behind-the-meter” generation to bypass the interconnection queues, transmission constraints, and substation bottlenecks slowing projects nationwide. The appeal is clear: speed-to-power and greater control over delivery timelines. But that speed shifts the project’s risk profile. Instead of navigating traditional utility procurement, the development begins to resemble a distributed power plant subject to industrial permitting, fuel supply logistics, air emissions scrutiny, noise controls, and groundwater governance. These are issues communities typically associate with generation facilities, not hyperscale data centers. Our earlier coverage focused on the technical and strategic logic of pairing compute with on-site generation. Now the story has evolved. Community opposition is emerging as a material variable that could influence schedule and scope. Although groundbreaking was held in November 2025, final site plans and key conditional use permits remain pending at the time of publication. What Is Actually Being Proposed? Public records from Millard County show Joule pursuing a zone change for approximately 4,000 acres (about 6.25 square miles), converting agricultural land near 11000 N McCornick Road to Heavy Industrial use. At a July 2025 public meeting, residents raised familiar concerns that surface when a rural landscape is targeted for hyperscale development: labor influx and housing strain, water use, traffic, dust and wildfire risk, wildlife disruption, and the broader loss of farmland and local character. What has proven less clear is the precise scale and sequencing of the buildout. Local reporting describes an initial phase of six data center buildings, each supported by a substantial fleet of Caterpillar

From Lab to Gigawatt: CoreWeave’s ARENA and the AI Validation Imperative

The Production Readiness Gap AI teams continue to confront a familiar challenge: moving from experimentation to predictable production performance. Models that train successfully on small clusters or sandbox environments often behave very differently when deployed at scale. Performance characteristics shift. Data pipelines strain under sustained load. Cost assumptions unravel. Synthetic benchmarks and reduced test sets rarely capture the complex interactions between compute, storage, networking, and orchestration that define real-world AI systems. The result can be an expensive “Day One” surprise: unexpected infrastructure costs, bottlenecks across distributed components, and delays that ripple across product timelines. CoreWeave’s view is that benchmarking and production launch can no longer be treated as separate phases. Instead, validation must occur in environments that replicate the architectural, operational, and economic realities of live deployment. ARENA is designed around that premise. The platform allows customers to run full workloads on CoreWeave’s production-grade GPU infrastructure, using standardized compute stacks, network configurations, data paths, and service integrations that mirror actual deployment environments. Rather than approximating production behavior, the goal is to observe it directly. Key capabilities include: Running real workloads on GPU clusters that match production configurations. Benchmarking both performance and cost under realistic operational conditions. Diagnosing bottlenecks and scaling behavior across compute, storage, and networking layers. Leveraging standardized observability tools and guided engineering support. CoreWeave positions ARENA as an alternative to traditional demo or sandbox environments; one informed by its own experience operating large-scale AI infrastructure. By validating workloads under production conditions early in the lifecycle, teams gain empirical insight into performance dynamics and cost curves before committing capital and operational resources. Why Production-Scale Validation Has Become Strategic The demand for environments like ARENA reflects how fundamentally AI workloads have changed. Several structural shifts are driving the need for production-scale validation: Continuous, Multi-Layered Workloads AI systems are no longer

GenAI Pushes Cloud to $119B Quarter as AI Networking Race Intensifies

Cisco Targets the AI Fabric Bottleneck Cisco introduced its Silicon One G300, a new switching ASIC delivering 102.4 Tbps of throughput and designed specifically for large-scale AI cluster deployments. The chip will power next-generation Cisco Nexus 9000 and 8000 systems aimed at hyperscalers, neocloud providers, sovereign cloud operators, and enterprises building AI infrastructure. The company is positioning the platform around a simple premise: at AI-factory scale, the network becomes part of the compute plane. According to Cisco, the G300 architecture enables: 33% higher network utilization 28% reduction in AI job completion time Support for emerging 1.6T Ethernet environments Integrated telemetry and path-based load balancing Martin Lund, EVP of Cisco’s Common Hardware Group, emphasized the growing centrality of data movement. “As AI training and inference continues to scale, data movement is the key to efficient AI compute; the network becomes part of the compute itself,” Lund said. The new systems also reflect another emerging trend in AI infrastructure: the spread of liquid cooling beyond servers and into the networking layer. Cisco says its fully liquid-cooled switch designs can deliver nearly 70% energy efficiency improvement compared with prior approaches, while new 800G linear pluggable optics aim to reduce optical power consumption by up to 50%. Ethernet’s Next Big Test Industry analysts increasingly view AI networking as one of the most consequential battlegrounds in the current infrastructure cycle. Alan Weckel, founder of 650 Group, noted that backend AI networks are rapidly moving toward 1.6T architectures, a shift that could push the Ethernet data center switch market above $100 billion annually. SemiAnalysis founder Dylan Patel was even more direct in framing the stakes. “Networking has been the fundamental constraint to scaling AI,” Patel said. “At this scale, networking directly determines how much AI compute can actually be utilized.” That reality is driving intense innovation

Meta scoops up more of Nvidia’s AI chip output

“No one deploys AI at Meta’s scale,” Nvidia CEO Jensen Huang said in a news release. Meta plans capital expenditure, mostly on data centers and the computing infrastructure they contain, of $115 billion-$135 billion this year — more than some hyperscalers, which rent their computing capacity to others. Meta is keeping it all for itself. This could be bad news for other enterprises, as the demands of the hyperscalers and big customers like Meta is leading to a decrease in the availability of chips to train and run AI models. IDC is predicting that the broader AI-driven chip shortage will have a significant effect on the IT market over the next two years as companies struggle to replace everything from laptops to servers. In particular, businesses looking for Nvidia processors may be forced to look elsewhere.

Microsoft will invest $80B in AI data centers in fiscal 2025

And Microsoft isn’t the only one that is ramping up its investments into AI-enabled data centers. Rival cloud service providers are all investing in either upgrading or opening new data centers to capture a larger chunk of business from developers and users of large language models (LLMs). In a report published in October 2024, Bloomberg Intelligence estimated that demand for generative AI would push Microsoft, AWS, Google, Oracle, Meta, and Apple would between them devote $200 billion to capex in 2025, up from $110 billion in 2023. Microsoft is one of the biggest spenders, followed closely by Google and AWS, Bloomberg Intelligence said. Its estimate of Microsoft’s capital spending on AI, at $62.4 billion for calendar 2025, is lower than Smith’s claim that the company will invest $80 billion in the fiscal year to June 30, 2025. Both figures, though, are way higher than Microsoft’s 2020 capital expenditure of “just” $17.6 billion. The majority of the increased spending is tied to cloud services and the expansion of AI infrastructure needed to provide compute capacity for OpenAI workloads. Separately, last October Amazon CEO Andy Jassy said his company planned total capex spend of $75 billion in 2024 and even more in 2025, with much of it going to AWS, its cloud computing division.

John Deere unveils more autonomous farm machines to address skill labor shortage

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More Self-driving tractors might be the path to self-driving cars. John Deere has revealed a new line of autonomous machines and tech across agriculture, construction and commercial landscaping. The Moline, Illinois-based John Deere has been in business for 187 years, yet it’s been a regular as a non-tech company showing off technology at the big tech trade show in Las Vegas and is back at CES 2025 with more autonomous tractors and other vehicles. This is not something we usually cover, but John Deere has a lot of data that is interesting in the big picture of tech. The message from the company is that there aren’t enough skilled farm laborers to do the work that its customers need. It’s been a challenge for most of the last two decades, said Jahmy Hindman, CTO at John Deere, in a briefing. Much of the tech will come this fall and after that. He noted that the average farmer in the U.S. is over 58 and works 12 to 18 hours a day to grow food for us. And he said the American Farm Bureau Federation estimates there are roughly 2.4 million farm jobs that need to be filled annually; and the agricultural work force continues to shrink. (This is my hint to the anti-immigration crowd). John Deere’s autonomous 9RX Tractor. Farmers can oversee it using an app. While each of these industries experiences their own set of challenges, a commonality across all is skilled labor availability. In construction, about 80% percent of contractors struggle to find skilled labor. And in commercial landscaping, 86% of landscaping business owners can’t find labor to fill open positions, he said. “They have to figure out how to do

2025 playbook for enterprise AI success, from agents to evals

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More 2025 is poised to be a pivotal year for enterprise AI. The past year has seen rapid innovation, and this year will see the same. This has made it more critical than ever to revisit your AI strategy to stay competitive and create value for your customers. From scaling AI agents to optimizing costs, here are the five critical areas enterprises should prioritize for their AI strategy this year. 1. Agents: the next generation of automation AI agents are no longer theoretical. In 2025, they’re indispensable tools for enterprises looking to streamline operations and enhance customer interactions. Unlike traditional software, agents powered by large language models (LLMs) can make nuanced decisions, navigate complex multi-step tasks, and integrate seamlessly with tools and APIs. At the start of 2024, agents were not ready for prime time, making frustrating mistakes like hallucinating URLs. They started getting better as frontier large language models themselves improved. “Let me put it this way,” said Sam Witteveen, cofounder of Red Dragon, a company that develops agents for companies, and that recently reviewed the 48 agents it built last year. “Interestingly, the ones that we built at the start of the year, a lot of those worked way better at the end of the year just because the models got better.” Witteveen shared this in the video podcast we filmed to discuss these five big trends in detail. Models are getting better and hallucinating less, and they’re also being trained to do agentic tasks. Another feature that the model providers are researching is a way to use the LLM as a judge, and as models get cheaper (something we’ll cover below), companies can use three or more models to

OpenAI’s red teaming innovations define new essentials for security leaders in the AI era

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More OpenAI has taken a more aggressive approach to red teaming than its AI competitors, demonstrating its security teams’ advanced capabilities in two areas: multi-step reinforcement and external red teaming. OpenAI recently released two papers that set a new competitive standard for improving the quality, reliability and safety of AI models in these two techniques and more. The first paper, “OpenAI’s Approach to External Red Teaming for AI Models and Systems,” reports that specialized teams outside the company have proven effective in uncovering vulnerabilities that might otherwise have made it into a released model because in-house testing techniques may have missed them. In the second paper, “Diverse and Effective Red Teaming with Auto-Generated Rewards and Multi-Step Reinforcement Learning,” OpenAI introduces an automated framework that relies on iterative reinforcement learning to generate a broad spectrum of novel, wide-ranging attacks. Going all-in on red teaming pays practical, competitive dividends It’s encouraging to see competitive intensity in red teaming growing among AI companies. When Anthropic released its AI red team guidelines in June of last year, it joined AI providers including Google, Microsoft, Nvidia, OpenAI, and even the U.S.’s National Institute of Standards and Technology (NIST), which all had released red teaming frameworks. Investing heavily in red teaming yields tangible benefits for security leaders in any organization. OpenAI’s paper on external red teaming provides a detailed analysis of how the company strives to create specialized external teams that include cybersecurity and subject matter experts. The goal is to see if knowledgeable external teams can defeat models’ security perimeters and find gaps in their security, biases and controls that prompt-based testing couldn’t find. What makes OpenAI’s recent papers noteworthy is how well they define using human-in-the-middle

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