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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Citing impacts from the Iran war, near-zero flows through the Strait of Hormuz, accelerating global stock draws, and expectations for a muted US production response despite higher prices, Enverus Intelligence Research (EIR) raised its Brent crude oil price forecast. EIR now expects Brent to average $95/bbl for the remainder of 2026 and $100/bbl in 2027, reflecting what it described as a persistent global oil flow imbalance that continues to draw down inventories. “The world has an oil flow problem that is draining stocks,” said Al Salazar, director of research at EIR. “Whenever that oil flow problem is resolved, the world is left with low stocks. That’s what drives our oil price outlook higher for longer.” The outlook assumes the Strait of Hormuz remains largely closed for 3 months. EIR estimates that each month of constrained flows shifts the price outlook by about $10–15/bbl, underscoring the scale of the disruption and uncertainty around its duration. Despite West Texas Intermediate (WTI) prices of $90–100/bbl, EIR does not expect US producers to materially increase output. The firm forecasts US liquids production growth of 370,000 b/d by end-2026 and 580,000 b/d by end-2027, citing drilling-to-production lags, industry consolidation, and continued capital discipline. Global oil demand growth for 2026 has been reduced to about 500,000 b/d from 1.0 million b/d as higher energy prices and anticipated supply disruptions weigh on economic activity. Cumulative global oil stock draws are estimated at roughly 1 billion bbl through 2027, with non-OECD inventories—particularly in Asia—absorbing nearly half of the impact. A 60-day Jones Act waiver may provide limited short-term US shipping flexibility, but EIR said the measure is unlikely to materially affect global oil prices given broader market forces.

Equinor begins drilling $9-billion natural gas development project offshore Brazil

Equinor has started drilling the Raia natural gas project in the Campos basin presalt offshore Brazil. The $9-billion project is Equinor’s largest international investment, its largest project under execution, and marks the deepest water depth operation in its portfolio. The drilling campaign, which began Mar. 24 with the Valaris DS‑17 drillship, includes six wells in the Raia area 200 km offshore in water depths of around 2,900 m. The area is expected to hold recoverable natural gas and condensate reserves of over 1 billion boe. Raia’s development concept is based on production through wells connected to a 126,000-b/d floating production, storage and offloading unit (FPSO), which will treat produced oil/condensate and gas. Natural gas will be transported through a 200‑km pipeline from the FPSO to Cabiúnas, in the city of Macaé, Rio de Janeiro state. Once in operation, expected in 2028, the project will have the capacity to export up to 16 million cu m/day of natural gas, which could represent 15% of Brazil’s natural gas demand, the company said in a release Mar. 24. “While drilling takes place, integration and commissioning activities on the FPSO are progressing well putting us on track towards a safe start of operations in 2028,” said Geir Tungesvik, executive vice-president, projects, drilling and procurement, Equinor. The Raia project is operated by Equinor (35%), in partnership with Repsol Sinopec Brasil (35%) and Petrobras (30%).

Woodfibre LNG receives additional modules as construction advances

Woodfibre LNG LP has received two major modules within a week for its under‑construction, 2.1‑million tonne/year (tpy) LNG export plant near Squamish, British Columbia, advancing construction to about 65% complete. The deliveries include the liquefaction module—the project’s heaviest and most critical process unit—and the powerhouse module, which will serve as the plant’s central power and control hub. The liquefaction module, delivered aboard the heavy cargo vessel Red Zed 1, is the 15th of 19 modules scheduled for installation at the site, the company said in a Mar. 24 release. Weighing about 10,847 metric tonnes and occupying a footprint roughly equivalent to a football field, it is among the largest modules fabricated for the project. Once installed and commissioned, the liquefaction module will cool natural gas to about –162°C, converting it into LNG for export. Shortly after the liquefaction module’s arrival, Woodfibre LNG received the powerhouse module, the 16th module delivered to site. Weighing more than 4,200 metric tonnes, the powerhouse module will function as a power and control system, receiving electricity from BC Hydro and managing and distributing power to the plant’s electric‑drive compressors. The Woodfibre LNG project is designed as the first LNG export plant to use electric‑drive motors for liquefaction, replacing conventional gas‑turbine‑driven compressors. The Siemens electric‑drive system will be powered by renewable hydroelectricity from BC Hydro, eliminating the largest operational source of greenhouse gas emissions typically associated with liquefaction, the company said. The project is being built near the community of Squamish on the traditional territory of the Sḵwx̱wú7mesh Úxwumixw (Squamish Nation) and is regulated in part by the Indigenous government. All 19 modules are expected to arrive on site by spring 2026. Construction is scheduled for completion in 2027. Woodfibre LNG is owned by Woodfibre LNG Ltd. Partnership, which is 70% owned by Pacific Energy Corp.

ExxonMobil begins Turrum Phase 3 drilling off Australia’s east coast

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The Golden Rule of the oil market: Understanding global price dynamics and emerging exceptions

Mark FinleyBaker Institute, Rice University In recent weeks, questions surrounding the oil market crisis have been framed around a core principle described as the Golden Rule of the Oil Market: it is a global market. When conditions change anywhere—positively or negatively—prices respond everywhere. That framework helps explain why gasoline prices are rising in the US despite limited direct imports from the Middle East and the US’s status as a significant net exporter of oil. It also explains why oil cargoes that Iran permits to transit the Strait of Hormuz reduce Iran’s leverage over global oil prices, and by extension over US consumers and policymakers concerned about prices at the pump. Alongside its own exports, Iran has allowed a handful of additional tankers to transit the Strait, including several tankers destined for China and LPG shipments for India. The greater the volume of oil transiting the Strait, the smaller the disruption to the global oil market and the less upward pressure on global prices. The same logic applies to US efforts to ease sanctions on Iranian and Russian oil cargoes already at sea, which are unlikely to provide meaningful relief for rising oil prices. Under the Golden Rule, those barrels—having already been produced and shipped—would have found buyers regardless of sanctions, with price discounts sufficient to offset the risk of US penalties, as has been the case for Russian oil since 2022. Exceptions The Golden Rule has described oil market dynamics effectively for decades. However, a small number of potential exceptions have begun to emerge. For now, those exceptions remain relatively inconsequential, though larger risks may be developing. The non-market player There are two ways that supply and demand can be equalized. In a global market, it is achieved by price changes. Prices rise or fall to ensure that there is

Return of the PTT: Poste Italiane looks to snap up telco TIM

Poste Italiane sees opportunities in reuniting with the former state-owned telecommunications business: “The creation of an integrated group strategic pillar for the national economy, Italy’s largest connected infrastructure with leading positions in financial and insurance services,” it said in a news release. The company is looking to build some complementary services. “The transaction aims to scale and enhance Poste Italiane’s platform by adding three significant assets: a nationwide fixed and mobile network, a leading position in the country’s cloud and data center infrastructure and the ability to offer secure and seamless connectivity to all stakeholders,” it said. Poste Italiane was already the largest stakeholder in TIM and, as the government is the largest stakeholder in Poste Italiane, we’re getting back to the status quo of the 1980s. There is no sign, however, of other European governments following suit.

Networking terms and definitions

Monitoring: DCIM tools provide real-time visibility into the data center environment, tracking metrics like power consumption, temperature, humidity, and equipment status. Management: DCIM enables administrators to control and manage various aspects of the data center, including power distribution, cooling systems, and IT assets. Planning: DCIM facilitates capacity planning, helping data center operators understand current resource utilization and forecast future needs. Optimization: DCIM helps identify areas for improvement in energy efficiency, resource allocation, and overall operational efficiency. Data center sustainability Data center sustainability is the practice of designing, building and operating data centers in a way that minimizes their environmental by reducing energy consumption, water usage and waste generation, while also promoting sustainable practices such as renewable energy and efficient resource management. Hyperconverged infrastructure (HCI) Hyperconverged infrastructure combines compute, storage and networking in a single system and is used frequently in data centers. Enterprises can choose an appliance from a single vendor or install hardware-agnostic hyperconvergence software on white-box servers. Edge computing Edge computing is a distributed computing architecture that brings computation and storage closer to the sources of data. That is, instead of sending all data to a centralized cloud or data center, processing occurs at or near the edge of the network, where devices like sensors, IoT devices, or local servers are located to process, analyze and retain the data. In short, it’s about processing data closer to where it’s generated, which is designed to minimize latency, reduce bandwidth usage,and enable real-time responses. Edge AI Edge AI is the deployment and execution of artificial intelligence (AI) algorithms on edge devices or local servers, rather than relying solely on cloud-based, more centralized, AI processing. This involves running machine learning models and AI applications directly on devices at the edge of the network. Some key aspects of edge AI include the

Data center poaching adds to staffing crisis

“You can’t just not have a pipeline and keep drawing from the same talent pool. It’s going to wane. It’s going to dwindle, and then eventually you’re going to be at a point where you are needing to upskill a bunch of people, rapidly all at once, and you don’t have enough senior experts to really pass on that information,” Weinschenk said. Shortages are shifting up the stack In 2023, Uptime data showed most staffing pain at junior and mid-level roles, particularly in facilities. Senior gaps were visible but less severe. By 2024, electrical expertise had become a pressure point, reflecting a broader trade shortage just as infrastructures densified and voltages increased. When asked which roles in the data center have the highest rates of staff turnover, respondents said: Operations junior/mid-level: 57% Operations management: 27% Electrical: 21% Cabling/IT: 20% Senior management/strategy: 12% Design: 7% None: 9% By 2025, a pattern emerged: Operations management roles overtook junior positions as shortage areas, Uptime reported, marking the arrival of the silver tsunami as highly experienced managers and engineers retire without enough trained successors to replace them. As more sites are built—often in regions with limited local expertise—operators are discovering they cannot simply hire experience indefinitely, Uptime said. The pool of ready-made experts is shrinking just as demand rises, according to its data. Poaching masks a deeper talent pipeline failure Uptime survey data revealed how heavily the sector leans on poaching. Roughly a quarter of staff departures are employees hired away by competitors; only a small amount of workers leave the industry entirely. Instead of investing in training and upskilling, many operators are rotating the same set of skilled people around the industry, hoping higher pay will keep them in place. Uptime said that this creates several long-term risks:

Panasonic says datacenter batteries are selling out and AI is to blame

AI servers are rewriting the power rulebook The root cause, Panasonic noted in the statement, is the electrical behavior of AI workloads. Unlike conventional server applications, AI inference and training draw large amounts of electricity in short bursts to sustain GPU processing, causing peak power levels to spike rapidly and voltages to fluctuate. “Peak power levels for such servers can rise rapidly, and voltages can often become unstable,” the statement said. “Securing stable, highly reliable power supplies is an absolute necessity for AI datacenters.” Vertiv warned in its 2025 Data Center Trends predictions that AI racks must handle loads that “can fluctuate from a 10% idle to a 150% overload in a flash,” requiring UPS systems and batteries with significantly higher power densities than current infrastructure provides. Panasonic said the solution gaining traction among hyperscalers is to place a battery backup unit on each server rack rather than rely on centralized UPS infrastructure upstream, absorbing voltage instability at the source. The company said its systems also carry a peak shaving function that stores off-peak electricity and deploys it during demand spikes, reducing peak grid draw at a time when AI-driven consumption faces growing regulatory and utility scrutiny. Several independent research bodies have reached similar conclusions on the severity of the power challenge ahead. Uptime Institute, in its Five Data Center Predictions for 2026, said “developers will not outrun the power shortage,” with research analyst Max Smolaks warning the crisis “is likely to last many years.” The IEA projected global datacenter electricity consumption could exceed 1,000 TWh by 2026, more than double 2022 levels, while Gartner has warned that energy shortages could restrict 40% of AI datacenters by 2027. Gogia said the shift runs deeper than a hardware swap. “This is not backup in the traditional sense. This is active stabilisation,”

Why AI rack densities make liquid cooling non-negotiable

Average rack power density has more than doubled in two years, from 8 kW to 17 kW, and is projected to reach 30 kW by 2027, according to anOctober 2024 McKinsey report, with AI training racks already well ahead of that average. Those limits show up in GPU clock speed. H100 GPUs under inadequate air cooling can throttle to a fraction of their rated clock speed within seconds of a sustained training run. In distributed jobs across thousands of GPUs, one throttled chip can stall the entire run. TheDOE estimates cooling accounts for up to 40% of data center energy use. JLL research establishes three density thresholds: Up to ~20 kW per rack: air cooling is adequate Up to ~100 kW: rear-door heat exchangers extend viability Above ~175 kW: immersion cooling is required Direct-to-chip cooling fills the middle band, handling densities between ~100 and ~175 kW where rear-door exchangers fall short and immersion is not yet warranted. Hot water changes the economics Mechanical chillers are one of the biggest energy draws in any liquid-cooled data center, and until recently there were an unavoidable cost of liquid cooling. Nvidia’s Vera Rubin processor is changing that. At CES in January 2026, Jensen Huang announced that Vera Rubin supports liquid cooling at 45 degrees Celsius, high enough for data centers to reject heat through dry coolers using ambient air rather than mechanical chillers.Nvidia’s CES press release confirmed Rubin is in full production, with customer availability in the second half of 2026. According toNvida’s product specifications, the Vera Rubin NVL72 uses warm-water, single-phase direct liquid cooling at a 45°C supply temperature, allowing data centers to reject heat through dry coolers using ambient air rather than energy-intensive chiller systems.

Executive Roundtable: AI Infrastructure Enters Its Execution Era

Miranda Gardiner, iMasons Climate Accord: Since 2023, the digital infrastructure industry has moved definitively from planning to execution in the AI infrastructure cycle. Industry analysts forecast continued exponential growth, with active capacity at least doubling between now and 2030 and total capacity potentially tripling, quintupling, or more. In practical terms, we’ll see more digital infrastructure capacity come online in the next five year than has been built in the past 30 years, representing a historic industrial transformation requiring trillions of dollars in capital expenditure and a workforce measured in the millions. Design and organizational flexibility, integrated execution of sustainable solutions, and community-centered workforce development will separate those that thrive from those that struggle. Effective organizations will pivot quickly under these constantly shifting conditions and the leaders will be those that build fast but build right, as strategic flexibility balances long-term performance, efficiency, and regulatory compliance. We already know the resource intensity required to bring AI resources online and are working diligently to ensure this short-term, delivering streamlined and optimized solutions for everything from site selection to cooling and power management while lower lifecycle emissions. Additionally, in some regions, grid interconnection timelines and power availability are already the pacing item for data center development. Organizations that align their sustainability targets and energy procurement strategies will have a clearer path to execution. An operational model capable of delivering multiple large-scale facilities simultaneously across regions is another key piece to successful outcomes. Standardized, repeatable frameworks that reduce engineering time and accelerate permitting. We hear often about collaboration and strong partnerships, and these will be critical with utilities, regulators, and equipment manufacturers to anticipate bottlenecks before they impact schedules. Execution discipline will increasingly determine competitive advantage as the industry scales. The world and, especially, our host communities, are watching closely. Projects that move forward

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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