```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <math.h>

__global__ void min_depth_softmax24_kernel(
    const float* __restrict__ input,
    float* __restrict__ output,
    const int depth,
    const int spatial)
{
    const int p = blockIdx.x * blockDim.x + threadIdx.x;
    const int batch = blockIdx.y;
    if (p >= spatial) return;

    const int64_t channel_stride = (int64_t)depth * spatial;
    const float* base = input + (int64_t)batch * 24 * channel_stride + p;

    float values[24];
    float maximum = -INFINITY;

    #pragma unroll
    for (int c = 0; c < 24; ++c) {
        const float* channel = base + c * channel_stride;
        float minimum = INFINITY;

        #pragma unroll 1
        for (int d = 0; d < depth; ++d) {
            const float value = channel[(int64_t)d * spatial];
            // Preserve NaNs throughout the minimum reduction.
            minimum = (value < minimum || isnan(value)) ? value : minimum;
        }

        values[c] = minimum;
        maximum = fmaxf(maximum, minimum);
    }

    float denominator = 0.0f;
    #pragma unroll
    for (int c = 0; c < 24; ++c) {
        values[c] = expf(values[c] - maximum);
        denominator += values[c];
    }

    const float reciprocal = 1.0f / denominator;
    float* destination = output + (int64_t)batch * 24 * spatial + p;

    #pragma unroll
    for (int c = 0; c < 24; ++c) {
        destination[(int64_t)c * spatial] = values[c] * reciprocal;
    }
}

torch::Tensor min_depth_softmax24_cuda(torch::Tensor input) {
    TORCH_CHECK(input.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(input.scalar_type() == at::kFloat, "Expected float32");
    TORCH_CHECK(input.dim() == 5 && input.size(1) == 24,
                "Expected shape [N, 24, D, H, W]");
    TORCH_CHECK(input.is_contiguous(), "Expected contiguous input");
    TORCH_CHECK(input.size(2) > 0, "Depth must be positive");

    const c10::cuda::CUDAGuard device_guard(input.device());

    const int64_t batches = input.size(0);
    const int depth = static_cast<int>(input.size(2));
    const int spatial = static_cast<int>(input.size(3) * input.size(4));

    auto output = torch::empty(
        {batches, 24, input.size(3), input.size(4)}, input.options());

    if (output.numel() == 0) return output;

    constexpr int threads = 128;
    const dim3 blocks((spatial + threads - 1) / threads, batches);
    min_depth_softmax24_kernel<<<
        blocks, threads, 0, at::cuda::getCurrentCUDAStream()
    >>>(
        input.data_ptr<float>(),
        output.data_ptr<float>(),
        depth,
        spatial
    );
    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_fused_ops = load_inline(
    name="conv3d_min_depth_softmax24_fused",
    cpp_sources=(
        "torch::Tensor min_depth_softmax24_cuda(torch::Tensor input);"
    ),
    cuda_sources=_cuda_source,
    functions=["min_depth_softmax24_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, dim):
        super().__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.dim = dim

    def forward(self, x):
        x = self.conv(x)
        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.is_contiguous()
            and x.size(1) == 24
            and self.dim in (2, -3)
            and x.size(0) <= 65535
            and not (torch.is_grad_enabled() and x.requires_grad)
        ):
            return _fused_ops.min_depth_softmax24_cuda(x)

        return torch.softmax(torch.min(x, dim=self.dim)[0], dim=1)
```