Add random source that matches PyTorch (#124)

* Add random source that matches PyTorch

This added random source that matches PyTorch on CPU. In particular, it
matches: `torch.randn([], dtype=torch.float)` result.

PyTorch's RNG is a bit convoluted and not claimed to be version-stable
(will open a separate issue in PyTorch repo on this). However, the
current implementation on CPU is fairly straightforward^*.

1. If it is less than 16 elements, it uses Gaussian distribution sampled
   from MT19937 for double + Box-Muller transformation.

2. If it is more than 16 (16 included), it first do uniform sampling
   with whatever the resulting data type would be (in this case, torch.float),
   and then apply Box-Muller transformation over 16-element segment at a
   type, treating the first floating-point and the 8th as a pair, so on
   so forth.

3. If it is not a multiple of 16, trace back from the end for 16
   elements and redo step 2.

* Update with configuration available in SwiftDiffusionCLI

* Fix the RNG is not passed into pipelineConfig.

Author: liuliu

…ft/StableDiffusion/pipeline/Random.swift …ffusion/pipeline/NumPyRandomSource.swiftswift/StableDiffusion/pipeline/Random.swift renamed to swift/StableDiffusion/pipeline/NumPyRandomSource.swift swift/StableDiffusion/pipeline/Random.swift renamed to swift/StableDiffusion/pipeline/NumPyRandomSource.swift

@@ -10,7 +10,7 @@ import CoreML
 ///  [NumPy's older randomkit.c](https://github.com/numpy/numpy/blob/v1.0/numpy/random/mtrand/randomkit.c)
 ///
 @available(iOS 16.2, macOS 13.1, *)
-struct NumPyRandomSource: RandomNumberGenerator {
+struct NumPyRandomSource: RandomNumberGenerator, RandomSource {
 
     struct State {
         var key = [UInt32](repeating: 0, count: 624)

swift/StableDiffusion/pipeline/RandomSource.swift

@@ -0,0 +1,6 @@
+import CoreML
+
+@available(iOS 16.2, macOS 13.1, *)
+public protocol RandomSource {
+    mutating func normalShapedArray(_ shape: [Int], mean: Double, stdev: Double) -> MLShapedArray<Double>
+}

swift/StableDiffusion/pipeline/StableDiffusionPipeline.Configuration.swift

@@ -37,6 +37,8 @@ extension StableDiffusionPipeline {
         public var disableSafety: Bool = false
         /// The type of Scheduler to use.
         public var schedulerType: StableDiffusionScheduler = .pndmScheduler
+        /// The type of RNG to use
+        public var rngType: StableDiffusionRNG = .numpyRNG
 
         /// Given the configuration, what mode will be used for generation
         public var mode: Mode {

swift/StableDiffusion/pipeline/StableDiffusionPipeline.swift

@@ -14,6 +14,14 @@ public enum StableDiffusionScheduler {
     case dpmSolverMultistepScheduler
 }
 
+/// RNG compatible with StableDiffusionPipeline
+public enum StableDiffusionRNG {
+    /// RNG that matches numpy implementation
+    case numpyRNG
+    /// RNG that matches PyTorch CPU implementation.
+    case torchRNG
+}
+
 /// A pipeline used to generate image samples from text input using stable diffusion
 ///
 /// This implementation matches:
@@ -157,7 +165,7 @@ public struct StableDiffusionPipeline: ResourceManaging {
                 throw Error.startingImageProvidedWithoutEncoder
             }
 
-            let noiseTuples = generateImage2ImageLatentSamples(config.imageCount, stdev: 1, seed: config.seed)
+            let noiseTuples = generateImage2ImageLatentSamples(config.imageCount, rng: config.rngType, stdev: 1, seed: config.seed)
             latents = try noiseTuples.map({
                 try encoder.encode(
                     image: startingImage,
@@ -168,7 +176,7 @@ public struct StableDiffusionPipeline: ResourceManaging {
         } else {
             timestepStrength = nil
             // Generate random latent samples from specified seed
-            latents = generateLatentSamples(config.imageCount, stdev: stdev, seed: config.seed)
+            latents = generateLatentSamples(config.imageCount, rng: config.rngType, stdev: stdev, seed: config.seed)
         }
 
         // De-noising loop
@@ -224,11 +232,19 @@ public struct StableDiffusionPipeline: ResourceManaging {
         return try decodeToImages(latents, disableSafety: config.disableSafety)
     }
 
-    func generateLatentSamples(_ count: Int, stdev: Float, seed: UInt32) -> [MLShapedArray<Float32>] {
+    private func randomSource(from rng: StableDiffusionRNG, seed: UInt32) -> RandomSource {
+        switch rng {
+        case .numpyRNG:
+            return NumPyRandomSource(seed: seed)
+        case .torchRNG:
+            return TorchRandomSource(seed: seed)
+        }
+    }
+
+    func generateLatentSamples(_ count: Int, rng: StableDiffusionRNG, stdev: Float, seed: UInt32) -> [MLShapedArray<Float32>] {
         var sampleShape = unet.latentSampleShape
         sampleShape[0] = 1
-
-        var random = NumPyRandomSource(seed: seed)
+        var random = randomSource(from: rng, seed: seed)
         let samples = (0..<count).map { _ in
             MLShapedArray<Float32>(
                 converting: random.normalShapedArray(sampleShape, mean: 0.0, stdev: Double(stdev)))
@@ -245,11 +261,11 @@ public struct StableDiffusionPipeline: ResourceManaging {
     ///   - diagonalAndLatentNoiseIsSame: Diffusions library does not seem to use the same noise for the `DiagonalGaussianDistribution` operation,
     ///     but I have seen implementations of pipelines where it is the same.
     /// - Returns: An array of tuples of noise values with length of batch size.
-    func generateImage2ImageLatentSamples(_ count: Int, stdev: Float, seed: UInt32, diagonalAndLatentNoiseIsSame: Bool = false) -> [(diagonal: MLShapedArray<Float32>, latentNoise: MLShapedArray<Float32>)] {
+    func generateImage2ImageLatentSamples(_ count: Int, rng: StableDiffusionRNG, stdev: Float, seed: UInt32, diagonalAndLatentNoiseIsSame: Bool = false) -> [(diagonal: MLShapedArray<Float32>, latentNoise: MLShapedArray<Float32>)] {
         var sampleShape = unet.latentSampleShape
         sampleShape[0] = 1
 
-        var random = NumPyRandomSource(seed: UInt32(truncatingIfNeeded: seed))
+        var random = randomSource(from: rng, seed: seed)
         let samples = (0..<count).map { _ in
             if diagonalAndLatentNoiseIsSame {
                 let noise = MLShapedArray<Float32>(

swift/StableDiffusion/pipeline/TorchRandomSource.swift

@@ -0,0 +1,152 @@
+// For licensing see accompanying LICENSE.md file.
+// Copyright (C) 2022 Apple Inc. All Rights Reserved.
+
+import Foundation
+import CoreML
+
+/// A random source consistent with PyTorch
+///
+///  This implementation matches:
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/core/DistributionsHelper.h
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/native/cpu/DistributionTemplates.h
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/native/cpu/DistributionKernels.cpp
+///  https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/core/TransformationHelper.h
+///
+@available(iOS 16.2, macOS 13.1, *)
+struct TorchRandomSource: RandomNumberGenerator, RandomSource {
+
+  struct State {
+    var key = [UInt32](repeating: 0, count: 624)
+    var pos: Int = 0
+    var nextGauss: Double? = nil
+  }
+
+  var state: State
+
+  /// Initialize with a random seed
+  ///
+  /// - Parameters
+  ///     - seed: Seed for underlying Mersenne Twister 19937 generator
+  /// - Returns random source
+  init(seed: UInt32) {
+    state = .init()
+    var s = seed & 0xffff_ffff
+    for i in 0..<state.key.count {
+      state.key[i] = s
+      s = UInt32((UInt64(1_812_433_253) * UInt64(s ^ (s >> 30)) + UInt64(i) + 1) & 0xffff_ffff)
+    }
+    state.pos = state.key.count
+    state.nextGauss = nil
+  }
+
+  /// Generate next UInt32 using fast 32bit Mersenne Twister
+  mutating func nextUInt32() -> UInt32 {
+    let n = 624
+    let m = 397
+    let matrixA: UInt64 = 0x9908_b0df
+    let upperMask: UInt32 = 0x8000_0000
+    let lowerMask: UInt32 = 0x7fff_ffff
+
+    var y: UInt32
+    if state.pos == state.key.count {
+      for i in 0..<(n - m) {
+        y = (state.key[i] & upperMask) | (state.key[i + 1] & lowerMask)
+        state.key[i] = state.key[i + m] ^ (y >> 1) ^ UInt32((UInt64(~(y & 1)) + 1) & matrixA)
+      }
+      for i in (n - m)..<(n - 1) {
+        y = (state.key[i] & upperMask) | (state.key[i + 1] & lowerMask)
+        state.key[i] = state.key[i + (m - n)] ^ (y >> 1) ^ UInt32((UInt64(~(y & 1)) + 1) & matrixA)
+      }
+      y = (state.key[n - 1] & upperMask) | (state.key[0] & lowerMask)
+      state.key[n - 1] = state.key[m - 1] ^ (y >> 1) ^ UInt32((UInt64(~(y & 1)) + 1) & matrixA)
+      state.pos = 0
+    }
+    y = state.key[state.pos]
+    state.pos += 1
+
+    y ^= (y >> 11)
+    y ^= (y << 7) & 0x9d2c_5680
+    y ^= (y << 15) & 0xefc6_0000
+    y ^= (y >> 18)
+
+    return y
+  }
+
+  mutating func next() -> UInt64 {
+    let high = nextUInt32()
+    let low = nextUInt32()
+    return (UInt64(high) << 32) | UInt64(low)
+  }
+
+  /// Generate next random double value
+  mutating func nextDouble() -> Double {
+    let a = next()
+    return Double(a & 9_007_199_254_740_991) * (1.0 / 9007199254740992.0)
+  }
+
+  /// Generate next random float value
+  mutating func nextFloat() -> Float {
+    let a = nextUInt32()
+    return Float(a & 16_777_215) * (1.0 / 16777216.0)
+  }
+
+  /// Generate next random value from a standard normal
+  mutating func nextGauss() -> Double {
+    if let nextGauss = state.nextGauss {
+      state.nextGauss = nil
+      return nextGauss
+    }
+    // Box-Muller transform
+    let u1: Double = nextDouble()
+    let u2: Double = 1 - nextDouble()
+    let radius = sqrt(-2.0 * log(u2))
+    let theta = 2.0 * .pi * u1
+    state.nextGauss = radius * sin(theta)
+    return radius * cos(theta)
+  }
+
+  /// Generates an array of random values from a normal distribution with given mean and standard deviation.
+  /// This simulates torch.randn([1, 4, 64, 64], dtype=torch.float), note that for dtype=torch.double, it
+  /// will be slightly different.
+  mutating func normalArray(count: Int, mean: Double = 0.0, stdev: Double = 1.0) -> [Double] {
+    // If it is smaller than 16 elements, Torch generates from Box-Muller transform directly.
+    // Note that even if this is used to generate Float, it will use Double underneath.
+    guard count >= 16 else {
+      return (0..<count).map { _ in nextGauss() * stdev + mean }
+    }
+    // Otherwise, Torch first fill a uniform distribution array, then do Box-Muller
+    // transformation over this array.
+    var data = (0..<count).map { _ in Double(nextFloat()) }
+    for i in stride(from: 0, to: count - 15, by: 16) {
+      for j in 0..<8 {
+        let u1 = 1 - data[i + j]
+        let u2 = data[i + j + 8]
+        let radius = sqrt(-2.0 * log(u1))
+        let theta = 2.0 * .pi * u2
+        data[i + j] = radius * cos(theta) * stdev + mean
+        data[i + j + 8] = radius * sin(theta) * stdev + mean
+      }
+    }
+    if count % 16 != 0 {
+      for i in (count - 16)..<count {
+        data[i] = nextDouble()
+      }
+      let i = count - 16
+      for j in 0..<8 {
+        let u1 = 1 - data[i + j]
+        let u2 = data[i + j + 8]
+        let radius = sqrt(-2.0 * log(u1))
+        let theta = 2.0 * .pi * u2
+        data[i + j] = radius * cos(theta) * stdev + mean
+        data[i + j + 8] = radius * sin(theta) * stdev + mean
+      }
+    }
+    return data
+  }
+
+  /// Generate a shaped array with scalars from a normal distribution with given mean and standard deviation.
+  mutating func normalShapedArray(_ shape: [Int], mean: Double = 0.0, stdev: Double = 1.0) -> MLShapedArray<Double> {
+    let count = shape.reduce(1, *)
+    return .init(scalars: normalArray(count: count, mean: mean, stdev: stdev), shape: shape)
+  }
+}

swift/StableDiffusionCLI/main.swift

@@ -69,6 +69,9 @@ struct StableDiffusionSample: ParsableCommand {
     @Option(help: "Scheduler to use, one of {pndm, dpmpp}")
     var scheduler: SchedulerOption = .pndm
 
+    @Option(help: "Random number generator to use, one of {numpy, torch}")
+    var rng: RNGOption = .numpy
+
     @Flag(help: "Disable safety checking")
     var disableSafety: Bool = false
 
@@ -126,6 +129,7 @@ struct StableDiffusionSample: ParsableCommand {
         pipelineConfig.seed = seed
         pipelineConfig.guidanceScale = guidanceScale
         pipelineConfig.schedulerType = scheduler.stableDiffusionScheduler
+        pipelineConfig.rngType = rng.stableDiffusionRNG
 
         let images = try pipeline.generateImages(
             configuration: pipelineConfig,
@@ -250,6 +254,17 @@ enum SchedulerOption: String, ExpressibleByArgument {
     }
 }
 
+@available(iOS 16.2, macOS 13.1, *)
+enum RNGOption: String, ExpressibleByArgument {
+    case numpy, torch
+    var stableDiffusionRNG: StableDiffusionRNG {
+        switch self {
+        case .numpy: return .numpyRNG
+        case .torch: return .torchRNG
+        }
+    }
+}
+
 if #available(iOS 16.2, macOS 13.1, *) {
     StableDiffusionSample.main()
 } else {