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; } Oil futures eased from recent highs Tuesday as markets reacted to comments from US President Donald Trump suggesting the war with Iran may be nearing its conclusion, easing concerns about prolonged disruptions to Middle East crude supplies. Brent crude had climbed above $100/bbl amid escalating tensions in the region and fears that the war could prolong disruptions to shipments through the Strait of Hormuz—one of the world’s most critical energy chokepoints and a transit route for roughly one-fifth of global oil supply. Prices pulled back after Pres. Trump said the war was “almost done,” prompting traders to reassess the risk premium that had built into crude markets during the latest escalation. The earlier gains were driven by the fact that the war had disrupted tanker traffic in the Strait of Hormuz, raising concerns about wider supply disruptions from major Gulf oil producers. While the latest remarks helped calm markets, analysts note that geopolitical risks remain elevated and price volatility is likely to persist as traders monitor developments in the region. Any renewed escalation could quickly send crude prices higher again.

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Smackover Lithium, a joint venture between Standard Lithium Ltd. and Equinor, through subsidiaries of Equinor ASA, signed the first commercial offtake agreement for the South West Arkansas Project (SWA Project) with commodities group Trafigura Trading LLC. Under the terms of a binding take-or-pay offtake agreement, the JV will supply Trafigura with 8,000 metric tonnes/year (tpy) of battery-quality lithium carbonate (Li2CO3) over a 10-year period, beginning at the start of commercial production. Smackover Lithium is expected to achieve final investment decision (FID) for the project, which aims to use direct lithium extraction technology to produce lithium from brine resources in the Smackover formation in southern Arkansas, in 2026, with first production anticipated in 2028. The project encompasses about 30,000 acres of brine leases in the region, with the initial phase of project development focused on production from the 20,854-acre Reynolds Brine Unit. Front-end engineering design was completed in support of a definitive feasibility study with a principal recommendation that the project is ready to progress to FID. While pricing terms of the Trafigura deal were kept confidential, Standard Lithium said they are “structured to support the anticipated financing for the project.” The JV is seeking to finalize customer offtake agreements for roughly 80% of the 22,500 tonnes of annual nameplate lithium carbonate capacity for the initial phase of the project. This agreement represents over 40% of the targeted offtake commitments. Formed in 2024, Smackover Lithium is developing multiple DLE projects in Southwest Arkansas and East Texas. Standard Lithium is operator of the projecs with 55% interest. Equinor holds the remaining 45% interest.

Equinor makes oil and gas discoveries in the North Sea

Equinor Energy AS discovered oil in the Troll area and gas and condensate in the Sleipner area of the North Sea. Byrding C discovery well 35/11-32 S in production license (PL) 090 HS was made 5 km northwest of Fram field in Troll. The well was drilled by the COSL Innovator rig in 373 m of water to 3,517 m TVD subsea. It was terminated in the Heather formation from the Middle Jurassic. The primary exploration target was to prove petroleum in reservoir rocks from the Late Jurassic deep marine equivalent to the Sognefjord formation. The secondary target was to prove petroleum and investigate the presence of potential reservoir rocks in two prospective intervals from the Middle Jurassic in deep marine equivalents to the Fensfjord formation. The well encountered a 22-m oil column in sandstone layers in the Sognefjord formation with a total thickness of 82 m, of which 70 m was sandstone with moderate to good reservoir properties. The oil-water contact was encountered. The secondary exploration target in the Fensfjord formation did not prove reservoir rocks or hydrocarbons. The well was not formation-tested, but data and samples were collected. The well has been permanently plugged. Preliminary estimates indicate the size of the discovery is 4.4–8.2 MMboe. Oil discovered in Byrding C will be produced using existing or future infrastructure in the area. The Frida Kahlo discovery was drilled from the Sleipner B platform in production license PL 046 northwest of Sleipner Vest and is estimated to contain 5–9 MMboe of gas and condensate. The well will be brought on stream as early as April. The four most recent exploration wells in the Sleipner area, drilled over a 3-month period, include Lofn, Langemann, Sissel, and Frida Kahlo. All have all proven gas and condensate in the Hugin formation, with combined estimated

IEA launches record strategic oil release as Middle East war disrupts supply

The International Energy Agency (IEA) on Mar. 11 approved the largest emergency oil stock release in its history, making 400 million bbl available from member-country reserves in response to market disruptions tied to the war in the Middle East. The coordinated action, agreed unanimously by the IEA’s 32 member countries, is intended to ease supply pressure and temper price volatility as crude markets react to disrupted flows through the Strait of Hormuz. “The conflict in the Middle East is having significant impacts on global oil and gas markets, with major implications for energy security, energy affordability and the global economy for oil,” IEA executive director Fatih Birol said. The release more than doubles the previous IEA record set in 2022, when member countries collectively made 182.7 million bbl available following Russia’s invasion of Ukraine. Under the IEA system, member countries are required to maintain emergency oil stocks equal to at least 90 days of net imports, giving the agency a mechanism to respond when severe disruptions threaten global supply. The move comes after crude prices surged amid concerns that the US-Iran war could lead to prolonged disruption of exports from the Gulf. Despite the planned stock release, traders remain uncertain about whether reserve barrels alone will be enough to offset losses if the disruption persists. IEA said the emergency barrels will be supplied to the market from government-controlled and obligated industry stocks held across member countries. The action marks the sixth coordinated stock release in the agency’s history and underscores the seriousness of the current supply shock. Earlier the day, Japanese Prime Minister Sanae Takaichi said that Japan might start using its strategic oil reserves as early as next week, citing Japan’s unusually high dependence on Middle Eastern crude oil.

Infographic: Strait of Hormuz energy trade 2025

BOEM: US OCS holds 65.8 billion bbl of technically recoverable reserves

The US Outer Continental Shelf (OCS) holds mean undiscovered technically recoverable resources (UTRR) of 65.8 billion bbl of oil and 218.43 tcf of natural gas, the US Bureau of Ocean Energy Management (BOEM) said Mar. 9. Based on current production trends, these undiscovered resources represent the potential for 100 or more years of energy production from the US Outer Continental Shelf (OCS), BOEM said. A large portion of undiscovered OSC resources is located offshore the Gulf of Mexico and Alaska, according to the report. The offshore Gulf holds 26.9 million bbl of oil and 45.59 tcf of gas, while offshore Alaska holds an estimated mean 24.1 million bbl of oil and 122.29 tcf of gas. Offshore Pacific holds a mean UTRR of 10.3 million barrels of oil and 16.2 trillion cubic feet of gas, the report said. Offshore Atlantic holds a mean UTRR of 10.3 billion barrels of oil and 16.2 trillion cubic feet of gas. The assessment also evaluates the impact of prices on hydrocarbon recovery. Alaska is particularly price-sensitive, with mean undiscovered economically recoverable resources (UERR) negligible until prices average $100/bbl and $17.79/Mcf. At those levels, the mean UERR stands at 6.25 billion bbl and 13.25 tcf. At $160/bbl and $28.47/Mcf, recoverable resources jump to 14.67 billion bbl and 58.78 tcf. In the Gulf of Mexico, the mean UERR is 17.51 billion bbl of oil and 13.71 tcf at average prices of $60/bbl and $3.20/Mcf, increasing to 20.51 billion bbl and 17.49 tcf at average prices of $100/bbl and $5.34/Mcf, respectively. BOEM conducts a national resource assessment every 4 years to understand the “distribution of undiscovered oil and gas resources on the OCS” and identify opportunities for additional oil and gas exploration and development. “The Outer Continental Shelf holds tremendous resource potential,” said BOEM Acting Director Matt Giacona. “This

Who’s in the data-center space race?

But not everyone is that optimistic. According to Gartner, space-based data centers won’t be useful for decades, so companies should focus on expanding capacity down here on Earth. “I honestly think the idea with the current landscape of putting data centers in space is ridiculous,” OpenAI CEO Sam Altman told The Indian Express in February. Current satellite computing can’t easily scale to data centers, agrees Holger Mueller, an analyst at Constellation Research. “Weight is still the restriction,” he says. “It’s the equivalent of you buying a tablet or small laptop to travel across Latin America versus putting in a data center in the Amazon. Different power requirements, investment, totally different setup.” Then there are issues like damaged solar panels from meteorite storms and satellite debris, he adds. “You would have to pay for operational redundancy, which is further investment.” “Data centers will be built where they are affordable,” he says. “I don’t see space happening soon. Remember the Microsoft submerged one? Crickets…” But he agrees that solar power is nice, though the sun is only visible from one side of the planet at any given time. And space is cold, he says. Cooling down in outer space In fact, space is very cold. Close to absolute zero cold. But vacuum is also a great insulator, and there’s no air to move the heat around. “You can’t convect heat away,” says Richard Bonner, CTO at Accelsius, a liquid cooling company. Bonner has worked on NASA research projects about the challenge of cooling in space and is very familiar with the problem. A small proportion of the heat might be turned back into useful electricity, but that’s not really a solution, he says, because computer chips don’t get quite that hot. Instead, heat is radiated. When an object warms up, it generates

Community Opposition Emerges as New Gatekeeper for AI Data Center Expansion

The rapid global buildout of AI infrastructure is colliding with a new constraint that hyperscalers cannot solve with capital or GPUs: local opposition. In the first months of 2026, community resistance has already begun reshaping the development pipeline. A February analysis by Sightline Climate estimates that 30–50 percent of the data center capacity expected to come online in 2026 may not be delivered on schedule, reflecting a growing set of constraints that now include power availability, permitting challenges, and increasingly organized local opposition. The financial stakes are already substantial. Recent reporting indicates that tens of billions of dollars in planned data center development have been delayed or halted amid community pushback, including an estimated $98 billion worth of projects delayed or blocked in a single quarter of 2025, according to research cited by Data Center Watch. What had been framed throughout 2024 and 2025 as an inevitable expansion of hyperscale campuses, gigawatt-scale power agreements, and AI “factory” clusters is now encountering a different kind of gatekeeper: the communities expected to host the infrastructure. The shift is already visible in project outcomes. Across the United States, multiple projects were canceled, blocked, or fundamentally reshaped in the opening months of 2026 due to organized local opposition. Reporting from The Guardian found that 26 data center projects were canceled in December and January, compared with just one cancellation in October, suggesting that community resistance campaigns are increasingly capable of stopping projects before construction begins. At the same time, local governments are responding to community pressure with moratoriums, zoning restrictions, and permitting delays that can stall projects long enough to jeopardize financing or push developers to seek more favorable jurisdictions. While opposition to data center development is not new, the scale, coordination, and success rate of these efforts suggest a structural shift in how

From Real Estate to AI Factories: 7×24 Exchange’s Michael Siteman on Power, Politics, and the New Logic of Data Center Development

The data center industry’s explosive growth in the AI era is transforming how projects are conceived, financed, and built. What was once a real estate-driven business has become something far more complex: an engineering and infrastructure challenge defined by power availability, network topology, and local politics. That was one of the key themes in this recent episode of the Data Center Frontier Show podcast, where Editor-in-Chief Matt Vincent spoke with Michael Siteman, President of Prodigious Proclivities and a longtime leader and board member within 7×24 Exchange International. Drawing on decades of experience spanning brokerage, development, connectivity strategy, and infrastructure advisory, Siteman offered a field-level view of how the industry is adapting to the demands of AI-driven infrastructure. “The business used to be a pure real estate play,” Siteman said. “Now it’s a systems engineering problem. It’s power, network topology, the real estate itself, and political risk—all of these factors that have to work together.” Site Selection Becomes Systems Engineering For much of the early data center era, location decisions revolved around traditional real estate considerations: available buildings, proximity to customers, and nearby fiber connectivity. That logic has fundamentally changed. “Years ago, the question was: Is there a building? Are there carriers nearby?” Siteman recalled. “Now it’s completely different. Power availability, network topology, community acceptance—these are the variables that define whether a site works.” Utilities themselves have become gatekeepers in the process. “You go to a utility and ask if there’s power,” he explained. “They might say, ‘We might have power, but you have to pay us to study whether we actually have power.’” In many regions experiencing rapid digital infrastructure expansion, the answer increasingly comes back the same: there simply isn’t enough grid capacity available. Power Becomes the Project In the gigawatt-scale era of AI infrastructure, power strategy has moved

Meta’s Expanded MTIA Roadmap Signals a New Phase in AI Data Center Architecture

Silicon as a Data Center Design Tool Custom silicon also allows hyperscale operators to shape the physical characteristics of the infrastructure around it. Traditional GPU platforms often arrive with fixed power envelopes and thermal constraints. But internally designed accelerators allow companies like Meta to tailor chips to the rack-level power and cooling budgets of their own data center architecture. That flexibility becomes increasingly important as AI infrastructure pushes power densities far beyond traditional enterprise deployments. Custom accelerators like MTIA can be engineered to fit within the liquid-to-chip cooling frameworks now emerging in hyperscale AI racks. These systems circulate coolant directly across cold plates attached to processors, removing heat far more efficiently than air cooling and enabling higher compute densities. For operators running thousands of racks across multiple campuses, small improvements in performance-per-watt can translate into enormous reductions in total power demand. Software-Defined Power One of the subtler advantages of custom silicon lies in how it interacts with data center power systems. By controlling chip-level power management features such as power capping and workload throttling, operators can fine-tune how servers consume electricity inside each rack. This creates opportunities to safely run racks closer to their electrical limits without triggering breaker trips or thermal overloads. In practice, that means data center operators can extract more useful compute from the same electrical infrastructure. At hyperscale, where campuses may draw hundreds of megawatts, these efficiencies have a direct impact on capital planning and grid interconnection requirements. The Interconnect Layer AI accelerators do not operate in isolation. Their effectiveness depends heavily on how they connect to memory, storage, and other compute nodes across the cluster. Industry analysts expect next-generation inference platforms to rely increasingly on high-speed interconnect technologies such as CXL (Compute Express Link) and advanced networking fabrics to support disaggregated memory architectures and low-latency

PJM Moves to Redefine Behind-the-Meter Power for AI Data Centers

PJM Interconnection is moving to rewrite how behind-the-meter power is treated across its grid, signaling a major shift as AI-scale data centers push electricity demand into territory the current regulatory framework was never designed to handle. For years, PJM’s retail behind-the-meter generation rules allowed customers with onsite generation to “net” their load, reducing the amount of demand counted for transmission and other grid-related charges. The framework dates back to 2004, when behind-the-meter generation was typically associated with smaller industrial facilities or campus-style energy systems. PJM now argues that those assumptions no longer hold. The arrival of very large co-located loads, particularly hyperscale and AI data centers seeking hundreds of megawatts of power on accelerated timelines, has exposed gaps in how the system accounts for and plans around those facilities. In February 2026, PJM asked the Federal Energy Regulatory Commission to approve a tariff rewrite that would sharply limit how new large loads can rely on legacy netting rules. The move reflects a broader challenge facing grid operators as the rapid expansion of AI infrastructure begins to collide with planning frameworks built for a far slower era of demand growth. The proposal follows directly from a December 18, 2025 order from FERC finding that PJM’s existing tariff was “unjust and unreasonable” because it lacked clear rates, terms, and conditions governing co-location arrangements between large loads and generating facilities. Rather than prohibiting co-location, the commission directed PJM to create transparent rules allowing data centers and other large consumers to pair with generation while still protecting system reliability and other ratepayers. In essence, FERC told PJM not to shut the door on these arrangements, but to stop improvising and build a formal framework capable of supporting them. Why Behind-the-Meter Power Matters Behind-the-meter arrangements have become one of the most attractive strategies for hyperscale

The Gigawatt Bottleneck: Power Constraints Define AI Data Center Growth

Power is rapidly becoming the defining constraint on the next phase of data center growth. Across the industry, developers and hyperscalers are discovering that the biggest obstacle to deploying AI infrastructure is no longer capital, land, or connectivity. It’s electricity. In major markets from Northern Virginia to Texas, grid interconnection timelines are stretching out for years as utilities struggle to keep pace with a surge in large-load requests from AI-driven infrastructure. A new industry analysis from Bloom Energy reinforces that emerging reality. The company’s 2026 Data Center Power Report finds that electricity availability has moved from a planning consideration to a defining boundary on data center expansion, transforming site selection, power strategies, and the design of next-generation AI campuses. Based on surveys of hyperscalers, colocation providers, utilities, and equipment suppliers conducted through 2025, the report concludes that the determinants of data center growth are changing in the AI era. Across the industry, the result is a structural shift in how data centers are planned, financed, and powered. Industry executives interviewed for the report say the shift is already visible in real-world development decisions. “We’re seeing a geographic shift as certain regions become more power-friendly and therefore more attractive for data center construction,” said a hyperscaler energy executive quoted in the report, noting that developers are increasingly prioritizing markets where large blocks of electricity can be secured quickly and predictably. AI Load Is Accelerating Faster Than the Grid Bloom’s analysis suggests that U.S. data center IT load could grow from roughly 80 gigawatts in 2025 to about 150 gigawatts by 2028, effectively doubling within three years as AI training clusters and inference infrastructure expand. That surge is already showing up in grid planning models. The Electric Reliability Council of Texas (ERCOT), which oversees the Texas power market, now forecasts that statewide

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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